Drive to Suspension Bridge, park Leigh Woods side of the bridge, walk across bridge, check out views, visit Camera Obscura, there is a small park nearby, kids love sliding down the rocks there and exploring the trails in the undergrowth.
Afterwards walk into Clifton Village, have brunch/lunch in the Primrose Cafe, afterwards mosy through the Clifton Arcade shops and the kids can check out the sweet shop. Have a drink in the White Lion pub in the Avon Gorge Hotel but sit on the terrace under the suspension bridge.
There are some lovely walks round there too (Paradise Bottom walk by Leigh Court or Abbots Pool walk in Abbots Leigh).
Clevedon is also a worth a visit, there is a good park there for kids, you can walk along the to the Victorian Pier (there is a little tea room on the end or you can get a coffee at 5 The Beach).
If you are in Weston, there is a nice near Uphill (by the hospital): www.uphillvillage.org.uk/visitorinfo.htm
Tyntesfield (National Trust property) is worth a visit too and Cheddar Gorge and Caves and the West Somerset Railway too.
Have fun!