I was in Nottingham for 6 years (1997 to 2003) and ran for the uni and the local club. Ignore all the stats on crime - it is, as someone else said, skewed by St Anns and the Meadows, but even the Meadows isn't too bad (I never went to St Anns). I never felt unsafe walking about the city. If you are from a decent sized city in the US you will laugh at how low the gun crime figures are in comparison.
Nottingham is a great city - 2 universities so plenty of students, nightlife has developed massively in last 5-10 years with lots of new bars/clubs. Sadly not actually 4 girls to every bloke (I was told this was true 100 years ago when women from the surrounding countryside would come to work in the lace factories).
The uni is on a campus about 2 to 3 miles outside the city centre - nicely landscaped etc. Excellent academic reputation and a good mix of people (both Exeter and Nottm have quite a few rugby playing private school (in the UK sense of the word) Oxbridge rejects, but there are not too many in Nottm). There are 12 halls of residence each with their own bar, adding in the student union bar (there used to be 2 separate ones) gives the "Campus 14" bar crawl.
The uni athletics club (www.nottsuniathletics.org) is among the most successful in the UK and is, as Chris says above, big and friendly catering for all abilities. The uni does not offer scholarships in the same was as e.g. Loughborough, St Mary's or UWIC, but always seems to attract good athletes. Nottm is also about 30 mins drive from Loughborough - we have had the odd elite athlete (eg Andy Graffin, Olympic semi-finalist 1500m in 2000) who studied in Nottm and trained at Loughborough, but there isn't really a need to.
The local club (Notts AC -
www.nottsac.co.uk
) is consistently in the top 10 in the country for men's distance running (4th in the National Cross Country last year, 7th in the National 12 stage road relays, 2nd in the National 6 stage road relays in 2005) and is in the British League on the track (despite having had a couple of relegations due to a shortage of field eventers). The track is a short bus ride from the campus, and some of the training in fact takes place at the university in the winter as the roads there have less traffic.
When I was there most of the serious runners at the uni trained with Notts AC, but I think that now the uni have their own group. Very few unis in the UK have their own coach (which I understand is the norm in the US) so I think they coach themselves, with some input from the personal coaches of the various athletes, but I may be wrong on this. The middle distance coach at Notts AC (Trev Muxlow) is excellent - athletes he has previously coached include Richard Hill and Chris Warburton. Under him I went from a 2:02 800 (aged 18) to 1:55 for 800m, 3:59 for 1500 and 9:29 for 3000m steeplechase.
I can't speak for Exeter, but hopefully that gives you some Nottingham info!