Warwick is nicknamed 'The Bubble' by many students, and with good reason. Everything you could possibly need is on campus/within walking distance and you could, if you so wished, never go off-campus and be quite content.
If you live in one of the more central accommodations (Whitefields where i am, Arthur Vick etc) you are between 30 seconds and 2 minutes walk from either the union where The Copper Rooms (the university nightclub/venue) is and about the same to Costcutters.
Tesco is a 10-15 minute walk from campus, less so if you live further out and is 24 hours.
As far as social life goes there is always something going on, not necessarily the clubbing scene, but the sheer number of sports and other societies can keep you busy every day if you want them to (which you won't, as a Law student).
If it's the nightlife you're interested in, there's POP! on a wednesday which is a cheesy night which the sports socieites 'circle' before (play drinking games) and Top B on a friday which is your typical club music, along with £1.50 pints, jaegerbombs, mixers, etc. Dotted in amongst these are less regular nights such as Transmission (indie), Crash (rock/heavy) and Pressure (Dnb/Dubstep). For example, this saturday i'm going to see Modestep in the union.
There's also a company called The Uni Express which you buy a ticket for that picks up lots of buses full of students and takes them off-campus to places such as Gatecrasher in Birmingham (highly recommended!). These cost around about £10 depending on where you want to go.
The main place for nightlife outside of campus, but you can get buses up until midnight, or 2am on some nights, is Leamington Spa. £2.35 on the U1 to leamington, typically £5 or less between 4-5 people sharing a taxi for the journey back. Smack and Evolve are the decent clubs in leamington, with plenty of bars to haunt such as the infamous Kelsey's!
There's also Coventry, which has Kasbah and some other nightlife, but Coventry in general isn't a very nice place, you'll find you will only go there if there's something you need there or for the train station.
Also, a tip for wherever you go: DON'T do like me and spend the first term clubbing most nights, you end up SO far behind and procrastinating on this forum to avoid the masses of Land Law notes you have to do for your exam on Wednesday