Things in the vicinity of Stonehenge/Bath that might be worth a look (if you're driving, if you're doing it by train, these won't be as feasible:
Wells - small Cathedral city, the cathedral is very pretty and it's just a nice little city in general, not far from from Bath
Avebury - similar stuff to Stonehenge but you can actually walk around it
Cheddar Gorge - amazing caves and the home of the cheese
London things -
If you have time, the Horniman Museum is really fun, though a little out of the way. The National Portrait Gallery, National Gallery, Tate Britain, Tate Modern are all worth a look if you like museums. Also worth doing is walking along the South Bank - between Tower Bridge and Westminster if the weather is nice, as the views are lovely.
Other unsolicited advice - Americans, in particular, seem to have a real thing for Stonehenge and Bath but, personally, I'd recommend a day trip to Oxford or Cambridge as more interesting/fun, not a day trip but Edinburgh is also very much worth spending time in and, if you're interested in castles, the Welsh border castles are gorgeous.