Thanks for the advice. Got back a bit ago.
In London we did Victoria & Albert Museum, British Museum, National Gallery, Tate Modern, Tower of London, St Pauls, Westminster Abbey, Covent Garden, Borough Market, Harrods, Trafalgar Sq., Leceister Square, Picadilly Circus, Buckingham Palace/changing of guards, St James Park, Hyde/Kensington Park.
As for tips we enjoyed everything we did. I would say if Modern Art isn't your thing just skip Tate Modern or just go up to the cafe and have tea with a view.
The weather wasn't great so we skipped Portabello Market and didn't see as many of the smaller sites since we bussed/tubed a lot. Our first hotel had us on the 17th floor with views of Hyde Park, Big Ben/Parliament, St Pauls, etc so we just skipped the Eye which would've been higher but maybe not worth the time commitment.
Spent about 4.5 hours at each of the museums we went to aside from Tate and got a fair amount of museum fatigue. Each of them seemed to have some kind of highlights guide, if pressed for time I'd do that and zip through. If it is something that really interests you try splitting it up over two days. I really wanted to go back to the British Museum a bit more refreshed for the areas I just zipped through but it didn't work out. Two 3 hour trips would've been much better than the one 5.5 hour trip we did. We also didn't do any of the paid exhibits, we didn't have enough time to do the permanent collection let alone extra.
For Tower of London go early and immediately to the crown jewels. The line by the time we left at about 1:30 was very long. Also absolutely do the Beefeater tour, I usually hate those kinds of things but it was well worth it.
Buckingham Palace was packed well before the changing of the guards but out of luck we wandered by while they were setting up on Birdcage Walk in front to of the Wellington Barracks. Even the bit we watched was quite long and repetitive (guy marches around, salutes, yells, another guy does it, repeat, group turns, more yelling, etc) so I don't think waiting for hours to watch it is a great use of time but the setup on the side was nice enough for us.
We had no bad meals but we did have a few mediocre meals that just came down to being too tired and beat to bother finding a good place to eat.
York was also excellent and a perfect break away from London. Since the York Minster was so much less crowded that St Pauls or Westminster it gave a lot more opportunity to just wander around inside and enjoy it.
