No worries
I don't think Exeter would be preferred that much to Nottingham, they're both Russell Group unis and pretty respected in my opinion. Law is one where it might make a difference, but even then you could mitigate it with the right extra-curriculars and work experience. The course being newer might be an issue for some people, but I don't think it would be a big issue.
I'm from Plymouth (or close by anyway), so my opinion of Exeter isn't exactly unbiased. It's a small city, and not very diverse. Lots of people have a good time there, but in the past the uni/SU have been accused of racism. I haven't heard anything recently, this was all about 5 years ago, but coming from London, I can see how you would find it a bit small town-ish.
As I say, lots of people have a great time there, so you just have to work out if it's the right fit for you. Are you visiting Exeter again, or just Nottingham?