Coming from someone who goes to DMU,
I recommend you do to NTU, they have a brilliant rep for law, one of the few universities in the country to offer the BPTC
However, I'll give you a bit of info on DMU,
DMU law school in reality is actually really good, the tutors and staff are all very helpful, the module choices are great! There are loads of societies at DMU and if there isn't one you like it is very easy to start a new society. The DMU gym is great and pretty cheap for what you get (I believe it's under £200 for the full year and less depending on what option you go for). Student accommodation is pretty standard (£104-135 a week on average in first year).
Nightlife is alright, I think it just depends on if you make good friends to have a good night out with as opposed to it being good or bad, the city isn't too expensive, everything is sort of within a mile of each other. Leicester and DMU are very very multicultural, lots of people from London attend DMU
The university campus had a recent revamp and it now looks incredible.
Also the library at DMU is brilliant, not to mention DMU is one of the few universities in the country to have a subject specific law library.
Both are good universities for law, It just depends you and how far you'd like to travel, traveling to London from Leicester is about 1hr - 1.5hrs and about £37