The assumption is that schools in white middle class areas are somehow better isn't exactly true. Also the assumption that living in a middle class, expensive area automatically means access to local schools isn't exactly true either. Bristol schools are hugely over subscribed and DD's school (not quite in Easton) had 3 applications for every place.
There are some really outstanding schools out of the Bishopston, Henleaze, Westbury catchment areas.
As far as social problems in St Pauls and Easton. It's true that St Pauls has a reputation for being a violent area stemming from drugs. Easton in the past few years has really turned into a vibrant ethnic area where there's a mosque and a church on the same street and people integrate. A friend of mine commented that it's turning into Notting Hill.
It's interesting that people are discussing where they chose to live in Bristol. My partner is from the area, and it's his home. Personally, I wouldn't move to Horfield, Bishopston as I like the proximity of the local train station (Stapleton) and access to main line train service to London and the cycle path. There's the Chocolate Factory that is being regenerated into a plaza, cycle houses plus the school with its new building plans.
As far as the 'rougher elements' phrase. I'd like to address this as it's so incredibly offensive for a number of reasons, namely as it's a generality. Address the issue, such as 'drug problem,' or whatever. yes, Stapleton Road does have more of a problem with drugs and violent crime (related) than for instance some areas of Clifton. However, there was a drug related shooting in Stoke Bishop a few years ago, so the idea that if one lives in a white area, one is immune, isn't true. And if you think that student flats in Clifton aren't full of drugs, then you are kidding yourself.
But the idea that these issues are imported to schools isn't quite true. My DD's class is balanced; boys/girls, summer born/winter born, ethnic profile. My DD is totally color blind. She asked if we celebrated Eid. She is happy to talk to her friends at school about Ramadan, Hindu holidays and Christmas. It's what the UK looks like rather than some homogenous white landscape.