Hi,
I can't answer all of your questions, sorry, but I'll have a go. I work at Exeter University and have spent time in Bristol and York (not much, mind).
If you are outgoing, sporty and friendly, you will have a great time anywhere. Those universities have large enough student numbers and student unions for you to find friends and sports to suit your interests.
York and Exeter are both campus universities, so it can be like living in a student bubble. Bristol is a civic university so the departments are spread around the city. It depends what you prefer I suppose.
Exeter University campus has got to be the most beautiful in the country. The architecture isn't all that, but it's seriously like being in a national park: it is an actual registered Botanic Garden. There are so many spots of natural and cultivated beauty. I love it. The city is nice enough (walkable from campus), with a generic High Street, a few interesting independent areas, plenty of parks, a lovely Cathedral and Quay, a somewhat bizarre museum, and, for some reason, about 6 train stations with links to everywhere. Places in Devon, Cornwall, Somerset and Dorset are all within easy reach.
In terms of nightlife, bear in mind that Exeter is really a glorified town, with a population of about 120 000, with a social scene to reflect that. There are club nights on campus and obviously the students make it more vibrant than a non-university town, but it's fairly tame and limited (personally I don't care but I am old!). There are a few theatres, small + medium music venues and loads of pubs and restaurants.
York is a bit bigger so there's probably a bit more going on (I don't know much about it to be honest). York the city is absolutely lush. It's a bit touristy but that's because it is so blimming gorgeous.
Bristol is the only one that really feels like a 'proper' city with about 420 000 population size. It's very pretty, on a grander scale than the other 2, with impressive architecture, a funky harbour and the spectacular suspension bridge in Clifton. I think it's probably the best for diversity of nightlife and it has a great vibe: a bit alternative and arty, but with something for everyone.
I think all unis have good reps, and are all much of a muchness. Bristol is traditionally the Oxbridge alternative, York has been near the top of most league tables for donkeys' years, and Exeter is the new kid on the block for being in the higher echelons, league table-wise. I've heard that some departments are a bit snotty and too big for their boots, but I don't know about languages. I think they attract really good students. For language departments (it depends which ones you're doing), check out subject tables.
Personally, if I had my time again, I'd choose Bristol for its vibrance, but it depends on your taste. I'd have to say that from my perceptions of Exeter students (I studied at Nottingham and Leeds, by the way), they seem a bit less culturally diverse, a bit more traditional-ish, if you know what I mean, but everywhere I go there's someone clutching sports equipment or in their club kit, so I think it's a very sporty place with a big sports-oriented social scene.