Spare time:
It's a fairly small city but you have all your usual things, there's a big cinema, a bowling alley, lots of shops, many pubs and decent transport links (direct trains to Southampton, Brighton, London etc).
Then there's all the lovely "we live on the coast" type things, there's Clarence Pier with a traditional funfair sort of thing (if you brave the rollercoaster Skyways, I salute you), mini-golf, a huge patch of grass on the seafront known as Southsea Common which you'll spend your entire summer on...
There's also the Portsmouth-specific things, some of which are worth a look at some point during your time here. There's the Spinnaker Tower at Gunwharf which everyone has to go up at least once, you'll get amazing views of all of southern Hampshire and the IOW. There's the Historic Dockyard with HMS Victory, HMS Warrior and the Mary Rose. Even if naval history doesn't particularly interest you, they're a good day, maybe when the family are visiting? There's also Old Portsmouth and the Round Tower which is just quite pretty and a nice wander on a sunny day.
It has basically everything you could want really. All the standard things for being with your mates, then art galleries and museums and stuff for when you're feeling posh and your family want to know that Portsmouth has more than a never ending supply of vodka redbull.
Shopping:
Shopping is essentially split into 3 (maybe 4) areas of the city.
Gunwharf Quays - This is the site down at the Harbour. It's where the cinema and bowling is, as well as about half the restaurants. It has a number of shops, most of them outlet versions of relatively expensive places (Karen Millen, Ted Baker etc). There's a French Connection, Superdry, Monsoon, Jack Wills etc and even in the nicer places you can sometimes pick up a good bargain. It's not exactly every day shopping but it's also quite possible to shop there without bankrupting yourself.
Commercial Road/Cascades - This is the main High Street in Portsmouth. It has all your typical high street shops - TopShop, Debenhams, New Look, Boots, Waterstones, M&S, Starbucks, H&M, Primark etc. There's a few things you'd have to pop to Southampton for (Zara for example) but most of your shopping can be done here. The shopping centre is called Cascades and is right in the centre of Commercial Road. Tesco is also just off Commercial Road and if you're in the Guildhall halls, that's where your shopping is most likely going to be from in 1st year. There's also Palmerston Road down in Southsea which is essentially a much smaller version of Commercial Road, not great but alright to pop along to if you happen to be living that way.
Albert Road - This is the more independent part of the city and where you'll find all the "vintagey" shops. There's quite a few clothes shops, at least 2 that sell jewellery, a couple of antique shops. Even if you're not really into that sort of scene, it's good for an hour or 2 of wandering along and if you ARE into it, then it's quite easy to find some bargains.
Pubs:
Oh so many.
Can't really give you recommendations until you know where you're living but there's a few Wetherspoons for when you want a cheap drink, some very nice places when you're feeling classier and a number of places with Sky Sports.
Nightlife is split into a million pubs, some chavvy bars on Guildhall Walk (you sort of learn to love them...), some established clubs (Liquid, TigerTiger, Jongleurs), a couple of gay bars (Marthas and HB), some more indie places (Scandals) and gig venues (Wedgewood Rooms, Guildhall, Eastney Cellars, the Pyramids). For such a small city (it's compact enough that you can walk across most of it within half an hour), there's a surprising amount of variation.
Anything else you want to know, ask away.
I've been around here most of my life so I'm probably one of the best to know.
(Plus I could really use the distraction from 3rd year work!)