Try your local library as there a several route guides publihed for Bristol and surrounding area. They may also be available on South Glos / Bristol council / Bath council websites as downloads. They used to be. Many local bike shops also have the free council maps available.
Nip into the Sustrans office next to College Green – they have loads of ride guides for local area and for all across the country. Most of the leaflets are free. Dont try to visit them on a weekend though, as they are shut when the most people could actually visit them for advice. they also have a website with downloadable guides.
A ride down the avon gorge to Portishead (or on to Clevedon if you are keen) is rather nice as you get to see Bristol docks, the gorge, suspension bridge etc. Several cafes round docks and in Portishead, plus Portishead park/’seafront’ which would be nice for a picnic (Waitrose near by!). You can combine it with a road route one way or the other if you want more traffic and hills. There is always the Bristol/Bath path, esp if anyone is a steam train/cafe fan or fancies the georgian architecture of Bath.
General strikes out into the countryside can be done from any point on the ring road if you are near the edge of the city.
All I can think of right now.