I can’t comment on either of the Universities in Birmingham, as I haven’t been to either, I did however grow up in Kings Norton and spent some time living in Aston so I’ll give some insight on the city as place to live/stay.
I will just mention the locations of the universities for clarity.
Birmingham City University used to be called ‘The University of Central England in Birmingham’ and most of there facilities are dotted within a 10-15 minute walk of the City Centre.
Aston University is also in the same area as Birmingham City University, and is also a short walk to Town
‘University of Birmingham’ is mainly located around the Selly Oak/Edgebaston area of the city, and has some gorgeous red brick architecture, most of there campuses are within short walk to local rail connections, including it’s own ‘University’ station, and is a short journey to the City with reasonably regular trains, usually about every 20 mins.
There are multiple options for nightlife.
If your in the Selly Oak area there are quite a few local pubs, and it’s not to far from Harborne if you fancy doing the Harbourne Run and visiting all 9/10 pubs along the high street.
In the centre of ‘Town’ (the local term for the City Centre) you have Broad Street and Hurst Street.
Broad Street has a number of restaurants, night clubs and several canals, can be a little pricy per pint at times, but is a reasonable night out.
Hurst Street is the LGBT+ area of the city, and has most of the local gay bars and clubs, a little cheaper than Broad Street, and some places have LGBT only nights.
For shopping there is The Bull Ring and Grand Central (The poorly named shopping centre above Birmingham New Street Station) for higher tier shops such as Barbour, Hugo Boss, Hobbs, River Island and Next, there are also various eateries and other higher end.
Next to The Bull Ring is ‘The Rag Market’ and the Food Hall which has loads of reasonable independents stalls, with everything from Fabrics to Hardware.
The food hall has loads of butchers, fishmongers and a few veg stalls, there might even be a spice bazaar if my memory serves me correctly, it’s been a few years I moved to the sea side.
Outside this, theres the outdoor markets, this is mainly fruit and veg, but occasion has more standard market stalls, sadly however the Wholesale Markets have been moved out of the town centre to help make space for HS2.
stores.
The Mail Box is another upmarket shopping centre, I’ve been inside once, you need generally need a 6 figure salary to buy anything from there.
There’s also the Custard Factory that’s a mix of shopping, along with some creative and digital office space, set in a gorgeous industrial building that used to make Birds Custard Powder.
Culture wise, there’s three main theatres in the town, along with a few smaller ones. The Hippodrome (Hurst Street), The Alexandra (Just off Hurst Street) and The Rep (Broad Street).
There’s are a few live music venues including The O2 Academy, The Symphony Hall and the ICC, as well as several smaller venues such as The Hare and Hounds.
Just off from the Rep is the new Central Library, with its gorgeous Hogwarts like reference library, a roof terrace (usually closed) and various other facilities including an amphitheater.
There’s also several museums and art galleries, including Birmingham Museum and Art Gallery (BMAG), and ‘Think Tank Science Museum’ and The Transport Museum (I actually think there are three of those) that all house some amazing exhibits.
Then there’s The National Trust: Back to Backs that’s showcase Victorian Birmingham with it’s restored houses and shops.
Not to far out of town, and accessible directly via train is The NEC, if you like home shows, car shows etc...
There’s loads of open green spaces dotted all over the place, including Cannon Hill Park, The Lickey Hills, Sutton Park (though not technically Birmingham) and so many more.
With regards to crime, personal safety etc, I rarely felt uneasy moving around alone, or with my boyfriend, but my sister did feel uneasy at times, and eventually moved away, overall it’s not much different to many major city’s in the UK.
The city is an amazing place to stay, and I sometimes wish I hadn’t moved down to Devon to be closer to my family.
I hope that’s of some useful information, even if it’s not specifically about the Universities.