Is it worth living in Patna for your college life?

I (18F) am born & brought up in Patna, currently in a drop year to prepare for NEET. I’ve always wanted to go to a veterinary college. Coming to my point, I’m not very good at studies, but i think I could get into the Bihar Veterinary College, Patna this year. i’m extremely sceptical because I will have to spend 5.5 years here in Patna, basically my whole college life (which is supposed to be happening). I also have an option of going into a private veterinary college in Jaipur, Amritsar & money is not a factor here. Anyone i ask, they tell me getting into a government college is worth everything. I had hopes of having a good & happening life because i don’t think we have alot of things to do here in Patna. or anything at all. It worries me alot because I did not see myself ending up here ever. What do you guys think, is getting a govt college & living in Patna a better option than going into a private college at some better place?