Just to add, Warwick University isn't in the centre of Coventry... it's actually on the outskirts, and many of the students live in a neighbouring town called Leamington (with a regular bus service to the university). As the uni is in the outer suburbs, it's definitely in one of the nicer areas of Coventry. However, there is also a nearby council estate called Canley which is very close to the university, but I'm not aware of any trouble between the students and the locals (it's Coventry Uni who they have their biggest rivalry with lol).
Yes, Coventry does have that reputation from years ago (no idea what it's like now), but due to the location of the Uni campus, you could avoid the city centre itself for 99% of the time you're there, if you wanted to.
And, as said above, just knowledge of the risks is 1/2 the battle in these kind of things.