I'm from Derby although I don't go to university there. I think the problem with Derby is that it is constantly overshaddowed by Nottingham, both in terms of the city and also the university. Being in Derby is annoying as you have Nottingham so close yet so far for shopping and nightlife. You can get the Red Arrow bus or train between the two and it only takes about 20-30 minutes, but having lived in Derby and been to college in Nottingham, I hate living on the Derby side of the two as the nightlife in Nottingham is so much better, in my opinion.
Also... please don't take this in a bad manner, as its not my personal opinion: Derby is often laughed at by people in the local area as a bit of a crap university, and where people only go if they can't get in elsewhere. There are loads of home students at Derby Uni (a lot of my friends go there) and most of them are there because they couldn't really be bothered to leave home or take the step to university, and Derby was a nice option. I live about 20 minutes from the city and I have friends who moved into halls there, and said all of their flatmates were from about half an hour from the university so they all went home every weekend. This might be difficult if you're coming from a different place as its a very local university. Locally, its sort of said that you can get into Derby with your eyes closed and all you have to do is send off a blank application. It is constantly compared to Nottingham, Trent, Sheffield and Hallam universities, and its generally assumed that you went to Derby as you couldn't get into one of these. Obviously, this is only an issue if you are bothered about the local reputation of the university but I felt I should mention it. Again, I don't share the opinion but it is the popular one in the area.
Is your course at the Buxton or City campus in Derby? As if its in Buxton I wouldn't come here. Buxton is nice if you're a pensioner wanting a lovely day out in the Peak District for a bit of fish and chips, but not really as a student!
One of my best friends applied to Lincoln and I went with her for the interview. It looked like a really nice city and I get the feeling it will have more to offer as it isn't as overshaddowed by somewhere such as Nottingham. Here, Notts and Derby are so close that all of the good stuff is only in Notts, whereas Lincoln is that little bit more independent and stands alone in the country so I would assume will offer more as people have further to go to get to the next big place.