I live in coventry and it isn't grim at all, its not as big as other cities surrounding us like birmingham or leicester, but in all honesty they themselves are quite "grim".
Coventry has amazing night life, restaurants, decent shopping facilites. It has the ricoh arena for sport and entertainment, there is also a casino. The center of the city has just been refurbished and modernized and is looking better as the time progressed.
Most of the student accommodation is in earlsdon or leamington, both amazing locations for night light and are both really safe and student orientated.
I think people that have never stepped foot in coventry need too in order to have their own opinions, especially those calling it "poventry" when it is one of the most up and coming cities in the midlands.
The area surrounding Warwick university is full of greenery and close to a large tesco, gym, restaurants, pubs, excellent travel links.