If you have a Potter Head then Cursed Child is great but it's two shows so is £££ and will take up an entire day.
We tend to stay fairly central in a Premier Inn which means we can pop back for a rest / cup of tea for an hour or so which is much better than when we stay further out and makes a big difference although rooms are slightly smaller. We stayed at the Farringdon one last time. Good access to various tube lines, St Paul's and a little parade of shops including a Sainsbury's local was useful for topping up with basics.
If you come part of the way (it only needs to be a couple of stops I think) on the train you can then benefit from 241 at key attractions.
London Eye is both a must do to say you've done it and also rubbish, SeaLife centre isn't worth doing it's the same as anywhere, Shrek is great, Tower of London is great, Getting off and climbing up the Monument at Pudding lane is cheap and worth it if your children have studied Great Fire of London. St James Park is good if they are older and like Good Omens.
National History Museum for the dinosaurs, Science museum for the hands on bit, and then Kensington Palace and the Princess Diana park if they are still Park age
British museum for the mummies.
A trip to Greenwich on the river boat, tunnel under the Thames, cutty sark, observatory and planetarium if that's still there. Again that's slightly further out and would be a day but great views of the city from the top of the hill.