Translation:Vanya got into a university in St. Petersburg.
I agree, I left out the 'a' and it said I was incorrect. I wouldn't use the 'a' because it doesn't sound right to me. Vanya got into university in St Petersburg sounds fine to me.
Why in English this city is called Saint Peterburg? Was Peter the first a saint?
Peter the Great named the city after Saint Peter, not after himself. The choice of a Saint to name a city after was unlikely a coincidence though :)
I'm an English speaker living in St. Petersburg, and I got this wrong because I wrote university of St. Petersburg. Then I realized the mistake. There is a U of SPB, but there are many other universities IN SPB. So, the 'in' is correct.