Wow...that's a tough call as there is so much to do...I would almost suggest you do it borough by borough. Just thinking that you should be able to get a 'scratch off' map for London (as you can for the world) so you can keep tabs on where you've explored!
Off the top of my head, and assuming you've not done these things with your DCs:
Locally, have you been to Southside House (in Wimbledon Village), think it's open from Easter (until October)? Windmill Museum, St Mary's Church in Merton Park (very old possibly even 1000 years, where Nelson used to worship).
Off the top of my head Docklands Light Railway (try to get a seat right at the front) to Greenwich always worth a starter trip with O2 Arena, the Maritime Museum, the tunnel walk under the Thames, Emirates Cable Car ride (a must), spectacular views over London (including the Olympic Park and Arcelor Mittal Orbit)) from up near Greenwich Observatory...the Cutty Sark in all its restored glory, a trip down/up the Thames from there to the Thames Barrier or the other way into London
The Vaults under Waterloo Station often has some great things going on including soon 'The Goosebumps' promenade play (adults and children's versions available).
Afternoon Tea at The Ritz, cocktails at The Savoy or drinks up in the restaurant in Tate Modern. A trip to foodie Borogh Market (expensive but amazing).
St Paul's Cathedral (crypt amazing and a walk round the whispering gallery - if you can stand heights - amazing), combined with walking around the City area, across the Millenium Bridge, Museum of London
Canary Wharf, Docklands Museum - amazingly beautiful with all the water...
Somerset House, Tower of London, Buckingham Palace (some parts are open to the public in summer months), the Wallace Collection (off Oxford Street), The Wellcome Collection (if you're interested in what it is to be human), the Clink Museum, The Foundling Museum, Edward Soane House.
Check out what art exhibitions are in town this spring/summer, pre-book tickets and go to one or more. Still rue the day I didn't pre-book to go to the David Bowie retrospective at the V&A and by the time I thought to do so it was too late :-(
Walking along the SouthBank from near Lambeth Palace all the way to the Design Museum, with a trip into the archive library (where you can watch TV and films from yesteryear) at the BFI.
3D film at the BFI Imax near Waterloo Station.
Shoreditch is worth a trip in its own right...
A trip to the Globe Theatre to see a play (and a tour)
Highgage Cemetery and Hampstead Heath (including visit to Kenwood House). Again great views over London but N/S this time.
A walk along the Grand Union Canal as far as you can go (once did from Paddington Basin up to Camden and beyond).
And that's just for starters, only scratching the surface...you might even want to do slightly nerdy things like take a trip round all of the London Underground...(I've lived here all my adult life and still haven't been to some of the farflung parts of the lines to the north of London.