Bath's lovely for sightseeing but not especially brilliant for kids, sorry!
If you're going to the Roman Baths, make sure you get the kids' audio guide which helps to bring all those dusty old stones and pillars a bit more to life!
Agree that the open-top bus tour is worthwhile. Head to Victoria Park if you all need a run-around - there's a massive playground there.
If the weather's nice, your best lunch option is to go to one of Bath's very nice sandwich shops (Scoffs is our favourite by Parade Gardens) and head down to the riverside by Pulteney Bridge for a picnic. Riverside Cafe on the steps down from the east side of Pulteney Bridge is nice too, with views over the weir.
We tend to eat at the chains if it's raining - Giraffe down in the Southgate Centre, Pizza Express (two in the town) etc. Jamie's Italian in Milsom Place is worth a visit if you're a Jamie Oliver fan.
If you're in Bath on Saturday 24th, there might be something worth seeing at the Children's Literature Festival - they have loads of famous authors coming along.
www.bathkidslitfest.org.uk
Hope you have a great visit!