Depending on the age of your DC (ie if they can easily walk for a while), it's not worth getting the underground for 2/3 stops in my opinion, especially if you're in a location where you can walk along the Thames.
We always enjoy spending the day in Westminster - you can walk around looking at the sights, ie Thames, Big Ben, Houses of Parliament, Cathedral, Downing Street, Horse Guards Parade, walking through St James Park and see Buckingham Palace the other end - all free. If money stretches, there's a cafe in St James Park, if not buy yourself a picnic lunch (will probably be cheaper in a supermarket near where you're staying) and have lunch on one of the numerous benches in St James Park.
Tate Modern is free, but we didn't find it that interesting.
If you're near the sky garden, it's free and nice to go up and look at the views. I'm sure the views are spectacular in the day, but we booked our slot in the early evening and it was lovely seeing London all lit up in the dark.