I'm in a similar situation. I'm a mature student (28) and have researched accommodation options thoroughly - both on-campus and private. I can say with certainty that on-campus accommodation is way overpriced. You pay pretty much the same amount for a measly single-room with ensuite as for a 1-bed flat in the City. It's not worth it. As a postgrad you should have your own place anyway.
You've got two options, really:
1) Flatshare: this is very cheap (how's £250-£300/month sound?) and especially for those who can't do without other people around them.
You can find flatshares on Gumtree (there's a special Nottingham section).
2) Renting your own flat. This is somewhat more expensive than flatsharing, but cheaper than (or costing at the very least the same as) accommodation in University Halls. You can get a decent 1 bed flat or studio for between £300 and £500/month. I have a spacious 1bed flat in the Lace Market (great area in the city centre) and pay £395/month.
You need to do some research first to get acquainted with the housing market here. The safest bet is to go through an agency, especially if you want to avoid all the hassle and save yourself some time. You pay some admin fees, though, but at least you're getting good quality, a standard contract and you're not likely to get swindled. There's an agency that caters only to students (you can find it on the Notts uni website), but I found the deals there a little more expensive than private agencies.
If you want to be close to the uni, I'd recommend staying either in Beeston (where the uni is), Radford, Lenton or even the Arboretum. City centre is great for shopping and for being close to all the action and all that Nottingham has to offer. However, it's about 3-4 km from the uni, but you can get to uni by bus (10 min maybe) or walking (30-45min).
Message me if you need further help.
Good luck. :-)