It depends how the time machines work
Unlike the question and some comments assume, the etymology of transport infrastructure has only a little to do with the mode of transportation, and much more to do the the organisation of the transport network. Let me give you some examples.
This implies that your time machines operate on a fixed route, and are stopping along it, much like a train station or the predecessors of general trading stations. If i could catch a machine to today + or - 6 months, and that's all, it would probably be referred to as a station.
This just implies a place where the time machines can depart and arrive. It says nothing else about the organisation of the transport network. It descends from the ancient Greek word for "course" and although it is predominately used for aircraft, it is also usable in the word "hippodrome" as in a course for horses. However, because most people have no need to go to a hippodrome or aerodrome, it is a somewhat archaic word, even though it fulfils a perfectly usable general description.
Implies time machines need a runway or field to operate. That's really all it tells you.
This means your transport infrastructure requires a commercial port authority to run. If it requires a dedicated company to run it, and keep it organised, safe and functioning, it is probably going to be a larger facility, handling larger volumes of passengers, freight or both. In the case of airports, all airports are aerodromes, but not all aerodromes are airports, because the small ones don't need a full sized port authority to run.
Implies it's a central station that services many destinations
Implies it's infrastructure predominantly designed to facilitate passengers or freight switching from one transport mode/route to another.
In summary, you need to think about how your time machines work, and how they fit with a larger infrastructure. How are your passengers arriving, where are they going to, and how much organisation the whole setup needs. Once you have that, you can pick a sensible word.