I can tell you a lot about Coventry as a city but I don't know all that much about the Uni.
I've lived here all my life, and honestly I'm only just starting to appreciate the city. A lot of redevelopment is going on, so although it may seem a bit grotty, it's getting better. Some parts of Cov are actually really beautiful (the parts that weren't blitzed during the war), it's just a case of finding them! Unfortunately most of Cov was rebuilt in the 60s (we were hit really badly in WWII) so a lot of the architecture is ugly.
Sports facilities: the Uni is really close to the main sports centre so yes, it's easy to get to and although I don't know much about prices etc. I can't see it being much.
City Centre generally has everything you would need in terms of shops, though transport links to Birmingham are great and it's only 20 minutes on the train so there's always that option. The railway station is, however, a little way out of town, so it's slightly inconvenient in that sense. No more than a 15 minute walk if you know the way though.
I've been on school trips to Cov uni before, and from what I've seen (really just the arts dept.) I can't say I was hugely impressed, though I know that Cov is seen as being excellent for some subjects and not so great for others, so I honestly have no idea about Sports Science!
I know I answered non-existent questions there but I hope it helped a little anyway!