I was a student in Birmingham (2001-2005). I lived in the city centre near the Mailbox and off Hagley Road in Edgbaston.
Like Hatter said, be careful where you look. The city centre was good and around the Mailbox felt safe and was nice, but a few streets away and it was rough.
I lived in Edgbaston, on the reservoir side of Hagley Road. It was a rough, my friend lived about a 5 min drive away and it was really nice.
It’s a good city which most people overlook in favour of the more trendy Manchester.