Live in Bristol. Have 2 and 4 year olds so slightly guessing what a 7 year old would enjoy.
Anyway, City Museum on Queens Square is good and free, sure everybody can find something of interest inside (mummies, planes, dinosaurs, stuffed animals etc.). Just opposite is a Wetherspoons (The Berkley) with a family area at the back which would be a good cheap place for lunch.
From museum a not too long walk (or number 8 bus) through the architectural splendor of Clifton to the gorge and suspension bridge. Nice place for a picnic if weather good and playground nearby.
Yes, a ferry to the far end of the harbour (the Novia Scotia, an olde worlde pub) and walk back would be good and not too expensive way to get a good overview of the water front. Down on the docks the Arnolfini has a couple of galleries of modern art – something to amuse everyone, for example click here
About 10 minutes walk from the Arnolfini on Corn Street is St Nicholas Market, a recently restored covered bazaar. There are some nice food stalls there and another Wetherspoons just down the road.
If it's a scorcher, just outside @Bristol in Millenium Square there are some lovely fountains which kids seem to love to play in. Just remember to take towels and swimming stuff.
If you've got a car you could visit St Werburghs city farm. There's a really funky cafe with a little playground.
Hope you can find all these places, if you need more help drop me a line.
Royston