Deadline for applications is mid-October so you will need to have an address in the relevant area by then. The Bristol City Council website has details about the process, and links to all the schools plus Ofsted reports etc here. Obviously details for September 2011 won't be up yet.
All the schools mentioned by RainRain are good (though I don't know about Horfield either). Others with a good reputation are the three in Clifton (St Johns, Christ Church, Hotwells) but it's very expensive to live round there. I know people with children at St Werburghs who are happy with it - though slightly apprehensive about what they can do at secondary level.
I hope someone else will come along who knows more about south/east Bristol.
Bishopston/Gloucester Road/St Andrews are nice areas to live in, very convenient, and homes on the west side of Gloucester Rd are mainly in catchment for Redland Green or Cotham secondaries (two of the only decent ones in Bristol). So that means loads of families have moved there and there are nowhere near enough primary school places to go around, specially as there are some well-thought-of ones like Bishop Road and Sefton Park.
If you google a few keywords like North Bristol primary schools oversubscribed etc you should be able to catch up on the whole saga (lots of kids without a place for reception in September this year, and talk of bussing them all over the city).
It does now look like planning permission is through for a new primary school on the old cricket ground (St Andrews, east side of Gloucester Road) to open, supposedly, in September 2010 - though who knows if that will actually happen.
I'd say do lots of research and then rent/buy as close as possible (ie within a few hundred metres) of the school you are going to put top. (Unless you are Catholic, that is: most of the top-of-the-tables schools in Bristol are Catholic, some of them in otherwise rather grotty areas, but of course you don't need to live quite so close if you pass the religious conditions.)
Good luck.