Nobody knows. Roman writer Pliny the Elder scoffed at the useless pyramids and considered many Roman buildings to be both greater and more useful. This implies that the taller and more impressive the Emperor built his tower the more the Romans would have complained about the waste of money unless it had some practical use as well.
If the emperor had a practical use for the tower then the Romans would have approved of it.
What sort of proportions would the tower have to have to be considered a tower and not a building? As tall as wide, twice as tall as wide?
1) I could imagine a city with a tall cliff at one side. There could be a tower perhaps hundreds of feet tall with a vast room in it used as a water tank maybe 100 feet in diameter and 100 feet high. An aqueduct would cross from the edge of the cliff to the tower and bring in water to the top of the water tank. The water would flow out the bottom of the water tanks, still at least fifty feet above street level, through pipes and be distributed around the city.
There could be a viaduct alongside the aqueduct so people could reach the top of the water tank. If the water tank had a concrete dome the walls would have to be very think, like 20 feet, and a ring of rooms about 20 feet wide could have been built on top of them to help buttress the dome. Or the water tank could have a flat wooden roof and rooms could have been built on it. Thus there could be rooms for parties on top of the water tank. And above the rooms could be a viewing platform that might be hundreds of feet above the city depending on how tall the water tank was and how high the water tank's bottom was above street level.
2) The Sanctuary of Fortuna at Palestrina built about 120 BC on a series of terraces on a hillside had a very impressive total vertical dimension. But I don't know what was the greatest height of open interior space as opposed to filled in terraces. Obviously an emperor could have built a similar structure which appeared to be a tower from the outside if it was built on narrow terraces on a narrow tall hillside.
3) The emperors built several platforms from the sides of the Palatine Hill on tiers of arches to support additions to the Palace. These platforms may have been 50 to 100 feet tall, and then palace buildings were built on top of them. Septimius Severus built the Septizodium or Septizonium in front of one such palace wing. Italian archaeloogist Rudolfo Lanciani believed the Septizodium had been seven 30 foot stories tall, and thus 210 feet tall, and had been built to screen that palace wing, that thus should have had a total height of 210 feet. Modern archaeologists believe the Septizodium was only three stories high.
4) Many medieval Italian towns and cities looked like Manhattan with many tall slender towers belonging to noblemen. The few remaining in Bologna out of about a hundred range from 32 meters (104.987 feet) to 97 meters (318.241 feet).
The Torre de Mangia in Siena is 102 meters (334.646 feet) tall. I would guess that a Roman Emperor could have built towers that tall.
5) The Donjon of the 13th century Chateau de Coucy was 35 meters (114.829 feet) in diameter and 55 meters (180.446 feet) tall. A Roman Emperor, with many thousands of times the wealth, could probably have constructed similar structures.
This plan of the donjon of Courcy shows it had three great rooms, one above the other.
6) That immediately makes me think of building a tower with three Pantheon sized rooms in it, one above the other, for a total height of 450 feet.
And then a fourth Pantheon room could have built on top, this time out of wood or at least with a wooden dome to save weight. The Romans could certainly build wooden domes with half the diameter of the Pantheon Dome, and so might have been able to build a Pantheon sized one. In fact I have read a theory that the original Pantheon of Agrippa had a wooden dome approximately the same size as the concrete dome of the present Pantheon.
If I was building such a building on top of a tower of Pantheons I would have inner and outer walls about 20 feet apart, the outer wall considerably higher than the inner wall, and build wooden domes on top of both the inner and outer walls. Since the outer doom would be 40 feet wider in diameter than the inner dome and would spring from a higher level there would be plenty of space between the two domes for wooden beans and trusses to connect and mutually support them.
And there would be space between the two domes for stairs leading up to the top and a viewing platform 600 feet high atop the tower of Pantheons. Of course, that building is imaginary and was never built.
7) The Colossus of Nero was a statue 106.5 Roman feet (30.3 meters or 99 feet) tall, or possibly 37 meters (121 feet) It stood in the vestibulum of Nero's Golden House, possibly a courtyard, or a niche in an exterior wall, or in a room. From Suetonius,
There was nothing however in which he was more ruinously prodigal than in building. He made a palace extending all the way from the Palatine to the Esquiline, which at first he called the House of Passage, but when it was burned shortly after its completion and rebuilt, the Golden House. Its size and splendour will be sufficiently indicated by the p137following details. Its vestibule was large enough to contain a colossal statue of the emperor a hundred and twenty feet high; and it was so extensive that it had a triple colonnade a mile long.
This translation certainly makes it seem like the colossus was inside a room.
I have read that Nero had a life size painting of the colossus made, and hung it in the atrium of a villa built by Caligula on the outskirts of Rome. If the atrium was a courtyard or room it should have had a wall at least 100 to 120 feet tall to hang the painting.
8) I once read that the palace buildings Caligula built on the Palatine were built of wood, unlike most masonry Roman buildings. How tall a tower could a imperial megalomaniac like Caligula have built out of wood, if he wanted to?
The Yongning Pagoda was described in Record of the Buddhist Monasteries in Loyang to be 90 Zhang high and 100 Zhang with the spire, or 330 meters (1082.68 feet), but in the commentary of the Waterways Classic "only" 49 Zhang or 163 meters (534.777 feet). Archaeologist Yang Honxun who excavated its foundations believed it was about 147 meters (482.283 feet) tall.
See discussion here, page 9, posts 88 and 89.
Note that the Great pyramid is 138.8 meters (455.38 feet) tall and was 146.5 meters (480.643 feet) tall when completed. The facing stones were loosened in an earthquake in 1305 and later carried away, and the pyramidion at the top is missing. So if Calgula wanted to he could probably have built a wooden tower hundreds of feet tall.
9) The Legendary tomb of King Lars Porsena of the Etruscan city of Clusium was described in a way hard to visualize. it was supposed to be 200 meters (656.168 feet) tall.
If an Etruscan King of a city state could build such a structure about 500 BC I guess a Roman Emperor could have built something just as tall - however tall it really was.
10) There were a number of important ports in the Roman Empire, like Ostia and Portus, the ports of Rome. The Romans could have built tall towers as light houses at those ports, as tall as the Pharos at Alexandria. The Pharos at Alexandria is believed to have been about 120 to 137 meters (393.701 to 449.475 feet) tall. Or 115 to 135 meters (377.297 to 442.913 feet) feet tall.
In fact the Romans did convert the Pharos from a tower seen by day to a light house that could be seen at night, and did build some other light houses. The Roman light house or Pharos at Dover, England now stands only 60 feet high.
Today the pharos is only a four-storey building at 19 metres or around 60 feet high with the top floor section being a medieval restoration, but originally it was six levels high at 24 metres or 80 feet and, maybe even eight levels high, according to some Roman historians?
The Tower of Hercules in Corunna, Spain is an ancient Roman lighthouse.
he Tower of Hercules (Galician and Spanish: Torre de Hércules) is an ancient Roman lighthouse on a peninsula about 2.4 kilometers (1.5 mi) from the centre of A Coruña, Galicia, in north-western Spain. Until the 20th century, the tower itself was known as the "Farum Brigantium". The Latin word farum is derived from the Greek pharos for the Lighthouse of Alexandria. The structure is 55 metres (180 ft) tall and overlooks the North Atlantic coast of Spain. The structure, almost 1900 years old and and renovated in 1791, is the oldest Roman lighthouse in use today.
The tower is known to have existed by the 2nd century, built or perhaps rebuilt under Trajan, possibly on foundations following a design that was Phoenician in origin. It is thought to be modeled after the Lighthouse of Alexandria. At its base is preserved the cornerstone with the inscription MARTI AUG.SACR C.SEVIVS LVPVS ARCHTECTVS AEMINIENSIS LVSITANVS.EX.VO, permitting the original lighthouse tower to be ascribed to the architect Gaius Sevius Lupus, from Aeminium (present-day Coimbra, Portugal) in the former province of Lusitania, as an offering dedicated to Mars. The tower has been in constant use since the 2nd century and is considered to be the oldest existing lighthouse in the world.
In 1788, the original 34 metres (112 ft), 3-story tower was given a neoclassical restoration, including a new 21 metres (69 ft) fourth storey.14 The restoration was undertaken by naval engineer Eustaquio Giannini during the reign of Charles III of Spain, and was finished in 1791.14 Within, the much-repaired Roman and medieval masonry may be inspected.
It is kind of disappointing that it was originally only 34 metres (112 ft) tall.
This article suggests that the lighthouse built by Claudius at Ostia was probably taller than the Pharos at Alexandria.
If that is correct then a Roman Emperor did build a tower more than 300 feet tall, possibly more than 500 feet tall. There would be rooms and stairs up to the highest floor, which would be used for working the light house and not for events, of course.
The Cordouan Lighthouse built 1584-1611 in France was 162 feet (49 meters) tall and had a kings apartment on the second story.
Thus it is always possible that the pharos at Ostia had rooms sometimes used for imperial events, lower than the light room.