London eye. Not cheap but definitely sit down!
If you want cheap I always find the area around St Catherine's dock near the tower of london/tower bridge is a great place to explore for free. Lots of boats to see up close, ducks to feed, walking along the river front, the locks to cross over that leads out into the thames and little crossings over different parts of the water. Lots to talk about and for your child to learn without realising they're learning. They also have giant stones which the children can climb on as they walk around. There's also one wall completely covered in modern art which we talked about for ages looking at the colours and shapes and deciding which bit of the mural we liked best. Plenty of benches for your partner to sit on while you do a circuit or two of the dock or to take a rest while you check out something.
Also have cafes etc there so you don't have to take a packed lunch and endless drinks(unless you want to keep costs down).
You can jump on the ferry boat there too and take a ride a couple of stops along and then walk back perhaps.
Just a short walk to the tower too. You don't have to go in to talk about the castle and you can walk right around it. My son (when aged 7) got a lot of pleasure simply chasing the pigeons and jumping up and down the steps in the pedestrian area in front of the tower. Plenty of places to sit there too so your partner can wait for you to get back to her.
Lots of little side things to explore and then come back too. For example there's a very small park (garden type) near there which you can detour through as you go around the castle walls. Also in one part you can see where they've excavated some of the ruined part.
A very nice way to spend a dry day. We went in january last time, cold, not so busy but still lots of fun.
Gilly