I'll be driving down, so either outside Bristol or in the city centre is fine with me.
Cabot Circus has a large car park, which is linked to the shopping centre by a walkway. It has about 2,000 spaces, though it costs £2.30 for the first hour and then £1 an hour for the next 6 hours (between 7 am and 5pm). More than 7 hours is £18, but if you park after 5pm, it's £2 for the whole night.