You'd be fine walking back to the City centre after the gig. Bristol is generally safe and the route back doesn't go through rough areas! Plus there will be a lot of people heading the same way (to the central bus station or Temple Meads train station).
If you want a pub, try the Tobacco Factory or the Lounge on North Street in Bedminster. Only 5 minutes walk from the stadium. Again, another safe area with taxis driving through all the time. Assuming the bars and pubs are open then you have plenty of choice to stop for a drink.
I'm going to the gig on Wednesday and I'm also a Bristol City season ticket holder. Apart from fans being idiots, there are very few problems linked to football matches these days so there'll be no trouble for music. Hope you have a great time!