Where to apply? (MIPT, HSE, MSU)

Question

IT education

The house is far from Moscow (I need a hostel), I have admission everywhere for the All-Russian Olympiad in Mathematics. I have not decided on my next profession, I have almost no skills other than solving Olympiad problems in programming. I really want to get a good mathematical education. I would like to engage in applied research tasks in the future.
What I choose from: Moscow State University (mekhmat) / HSE (matfak / cs) / MIPT (FUPM / FIVT).
Moscow State University:
+ Dormitories near the academic building, in Moscow
+ Plenty of free time
- Specialist. After four years of study, having decided on further development, it will not be possible to leave.
Some complain about the outdated program, they say that they may not be successful with teachers. Although for the sake of mathematics, you can also go to NMU.
HSE:
+ modern mathematics at a very high level (in the case of mathematics)
+ quality of hostels
- distance from hostels to the university (1.5 hours in total by minibus + train + metro)
They say that mathematics there is quite strongly concentrated around such areas as algebraic geometry and mathematical physics. I'm not sure I'll need them much in the future.
Unfortunately, I don't know anything about MIPT.

Answer 1

Before entering such universities, look at this - ni.kprf.ru/n/2263
If ​​you still decide to go to IT - that is, ShAD and similar things.