A lot of the posts here which have advised not to go seem to be from people who lived there some years ago. No doubt the city has had many problems, particularly through the 70s and 80s after the car industry collapsed, leading to high unemployment and all the associated issues a damaged economy brings.
However since the 90s, and particularly in the last couple of years, investment has been pouring into the city. The Bullring Shopping Centre, Brindley Place, New station, new library, potential for HS2, regeneration of the Jewellery Quarter and a general lifting in incomes and living standards has really improved the city centre. There is a lot more regeneration planned too under the Big City Plan
https://bigcityplan.birmingham.gov.uk/ You can run or cycle along canals right into the countryside and they've recently renovated many of the cycling paths with a central government grant.
In the periphery, particularly to the south you'll find wide leafy avenues and large green open spaces which most people aren't aware of due to them normally driving in from the M6/A38 which is still a bit of a concrete jungle. Depending what you're into, Digbeth has a massive dance music scene with loads of events on at the former Custard Factory and Rainbow Venues. One of my favorites was City of Colours, a street art festival where they touch up some incredible street art.
http://www.birminghammail.co.uk/whats-on/arts-culture-news/city-colours-street-art-festival-11442603. There's also the National Indoor Arena which has loads of events, International Conference Centre/Symphony Hall for events and classical music, several theatres and the National Exhibition Centre near the airport for bigger events and conferences. There really is loads going on all the time which is what I love about the city.
The other thing is food and there is a massive selection. Our favourite curry place was Diwan Balti between Moseley and Basall Heath. There's also Blue Nile which is a great Ethopian in the Jewellery Quarter.
I saw it very much like a cheaper, smaller version of London.
Obviously as with every city there are rougher areas, particularly to the north, but to be honest the city is so sprawling you'd be unlikely to have to go there really.
I lived in Kings Heath for the last 4 years (moving away in February). Cheaper than Moseley (which is more hipster), less studenty and yummy mumy than Harbourne but still nice. If you might be working at the QE and have a bit of money behind you Harbourne is still nice. Its not really the student area as such, that's Selly Oak, but it does have a fair few postgrad students because it is so close to the uni. It has a nice vibe though with lots of pubs and bars.
The city has such a bad reputation and I really don't know why, I loved living there and if it wasn't for a family issue coming up, I'd still be there now!