Just considering gravity, it would be practical to build building to one third the height of building on Earth. But the limits are probably not what you expect. I will discuss all limits in terms of 1G, so you can divide by 3. This will be accurate ignoring second order effects like wind shear, vibration modes, etc. As your building will be shorter, they will naturally be stiffer than earth buildings. This is not always a good thing — earthquakes make building flexibility a good thing. Back to the finite element modeling for optimal designs.
The most common types of materials for modern build construction are wood, concrete/brick/masonry and steel. Based on the description of your world, you are not really high-tech, so you really won't be able to build quite as tall since you won't have modern computers to optimize designs, e.g., finite element analysis, etc. nor will you have the highest strength and durability for your steel and concrete.
In the US, wooden housing is limited to 5 stories, but this is more a limitation due to fire codes than the ultimate strength of wood. Taller wooden structure have been built. The tallest surviving ancient wooden pagoda was built in 1056 and is over 200 feet tall. But this is far from the possible limit as should be obvious since the tallest living tree is over 379 feet tall. For trees, the limiting factor is not the strength of wood. At least one group has designed a full sized wooden version of the Empire State Building 1250 feet tall.
A number of architects have designed steel buildings over 1 mile in height, some even over 1.5 miles tall.
Masonry, etc. is not quite as good for tall buildings, but you've probably heard of the Washington Monument, the tallest stone structure over 555 feet tall.
The real limitations are making the building useful, and cost effective. 5 stories is a practical limit for desirable buildings unless you have elevators. Fire fighting limits height to about 100 feet when ground based. More water pressure will not help as the firefighter can not control a hose with higher pressure.
Do you know how to design a sprinkler system that will work for a sky scraper. Do you know how to build water systems that will lift to great height but not blow someone off the toilet on the ground floor? HVAC is different when it has to span great height differences. Do you know how to construct tower cranes? Most of these things had some hard lessons along the way. Just learning how concrete pours and cures on a large scale is enough to cause you grief.
Building high is expensive, it only makes sense because land costs in dense cities is so high.
So, I would suggest you consider the highest building we have (or perhaps could build), divide by 3 and use that as a guideline. I could assume that your heavy worlders would be stronger, so they could still climb a 5 story building or operate a fire hose to 100 feet under triple gravity, but that is more a question for you to ponder.
Now, if you can raise the tech level well beyond ours, you can build your building out of diamond. Nothing is better, when diamond manufacture is cheap. Since diameter is brittle, it is not as strong as many engineering materials (you bend it, it breaks) but since ultimate strength will depend on occlusions and irregularities in the crystal structure, I will not calculate just how high a building you could be, but since it both lighter than steel and less compressible, but I am sure it would be impressive. I've seen the news stories about new materials stronger than diamond too, so maybe Lonsdaleite, Fullerite, wutzite boron nitride, carbyne or something else would actually be better than diamond for constructing the tallest skyscraper.
In a sky scraper, you basically ignore such things are arches, etc. as you don't want 100 foot ceilings without supporting columns. The arch and dome are excellent for the high ceiling effect, but they have no place in skyscraper as shear effects would tend to topple any tall structure lacking lots of cross bracing.
Decorative elements are clearly fair game. They usually weigh only a small fraction of the supporting structure. You want to erect a 50 foot solid gold statue, of course you will have problems. But decorations similar to what we typically see on building would not be problem.
Just how strong is wood? Characterizing strength and fracture of wood cell wall through uniaxial micro-compression test 160 MPa in compression. Compare this to A36 structural steel, 250 MPa minimum yield strength. Now wood is not 64% as strong as steel in bulk, but the cellulose fiber is remarkably strong for an organic molecule.
Not directly related to the topic, but ...
There has been some discussion re: limitations of tree growth. @VilleNiemi remarked that it was limited by water transport. Correct, in particular it is limited by capillary action. The speculation that under triple gravity the height limit would be unaffected is likely incorrect. The pressure of the water column would be 3 times that on earth. But the properties of water related to capillary action would not be changed, so the capillary action would only be able to lift water to 1/3 of the height.
In actual trees, capillary action is complicated by branching which allows water to rise higher than otherwise possible by have smaller "tubes" at the top of the tree than at the bottom. Also osmotic pressure is thought to assist liquid transport to allow taller trees. Osmotic pressure would not change based on gravity either, so even with an osmotic assist, expect upper bound on tree height to be about 1/3 in triple gravity.