Do you want to stay in the UK or are you willing to venture over to someplace like Paris. It's a fabulous city and there is just so much to see and do. The Eurostar is a great way to travel but you would have to check as I know that one of the tracks is closed for repairs after the fire the other week, so trains are not currently running a complete schedule.
Would your daughter be interested in a trip to Bath, there is so much great Roman history there, the open top bus tour is interesting. Then there is Portsmouth with the old navel ships.