Life on campus is great in my opinion. I don't really go out much but when I have the city has been absolutely fine and I've never heard anything negative from friends - only what great nights they've had. Public transport is easy, frequent and cheap (£1 for students) and taxis are similar as long as you go with registered ones obviously. Notts is like any other major city, I was worried just like you, yes there is crime but I've not experienced any since living here and neither has anyone I know, including some third years
I absolutely love it here and I have anxiety so I'm sure you'd be fine! My friends live in Broadgate park and they love it there too, good self catered, clean, warm, fix any troubles quickly, near to campus (20 minute walk to the centre max), shop on site but then close to Beeston town centre for actual supermarkets. Couldn't recommend the uni or the city more - so much to do and places to go and it's so easy to get around.
Again with regards to crime you just need to have standard common sense...don't wander about on your own, especially not drunk, keep valuables on you, get taxis in groups etc. you're unlikely to come to harm
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