Base in London and day trip from there. Research train routes and costs now. Advance tickets will be much cheaper than day of…
Also look at London Walks (www.walks.com). They do a Stonehenge trip.
Lots of things to do in London.
Markets: Spitafields, Borough, Portobello Road, Truman Brewery to name a few. Mercardo Mayfair is interesting.
Check on line for same day 1/2 price theatre tickets.
https://officiallondontheatre.com/tkts/ (M
Meander about Spitalfields, Camden Lock Market, Carnaby Street, Portobello Road and the Food Court at Harrods.
Attend an Evensong.
Countless free museums. Wonderful gift shops and cafes inside them.
Walk along the Thames path. Have a pub lunch ( and yes children are allowed in pubs…so are dogs)
Look for the green parrots in Hyde Park. Or the fallow deer in Richmond Park.
Tour Highgate Cemetary to see Karl Marx’s tomb.
You will not be bored in London.
Book your accommodations now. Check availability at Premiere Inn at County Hall , Victoria, Blackfriars or Southwark.
Check The Londonist and Timeout London websites to see if there are any shows, exhibitions, events, etc that might be happening during your travel dates.
Great city. Enjoy it.