Please check my daily plans

Here's a few suggestions for you to consider:
No theatre? How about a matinee - I think those happen on Wednesdays, but check theatremonkey.com to find out. Our son, at that age, really enjoyed both Phantom and Les Miserables, if either of those is still playing. On the south bank of the Thames, a bit past the London Eye, is the Globe Theatre. The tour is worthwhile, especially since your sons will soon study Shakespeare if they haven't done so already. Afterwards, walk across the Thames on the pedestrian bridge which leads to St. Paul's Cathedral. (Reminds me of that lovely bird-feeding scene from Mary Poppins.)

The Changing of the Guard really is not worth the bother. it's almost impossible to see anything unless you get there at least an hour early and stand around waiting and waiting and waiting.

The British Museum is fascinating - where else can you see the Rosetta Stone, the Sutton Hoo marbles, and the marble frieze which once adorned the Parthenon?

If any of you are Sherlock Holmes fans, you might enjoy the Sherlock Holmes pub for dinner or lunch. The second floor has an exhibit room which is a mockup of the famous 221B parlor.

A good source for picnic fixings is Simply Food, a branch of Marks and Spencer. They have numerous locations around town.

You might enjoy giving yourself a little break, letting the boys and their father go to the Natural History Museum while you go wander around in the nearby Victoria and Albert.

Greenwich is interesting and the boat trip down the Thames is really enjoyable.

yes I wanted to take them to see Wicked on Wednesday... just don;t know if I can fit it!! :)

Too many things... need more days!!

Sorry, what is IWM?

The changing of the guard is interesting at St. James's Palace. Smaller, quieter, but full of ceremony. Easier to manage than the huge, huge fray in front of Buckingham Palace. If you do a Google on St. James', the large red bricked courtyard on Marlborough Road is where the "new" guards come out and assemble. There's usually several tour groups in the area, so if you eavesdrop (everyone does), you will get a bit of information on what you are seeing!

It's a zoo in front of the Palace. And nothing to see unless you stake out a fence spot at the crack of dawn.

Also, I meant to say, be flexible. Westminster Abbey closes occasionally.

I think it looks pretty good. You've done a good job planning rest in. I do think the boys would love Greenwich.``

The Science Museum might be more fun for boys that age. Space ships and cars and lots of technology, etc. It's right next to the Natural History Museum.

The city is all lit up at night, and an evening walk along the South Bank is always fun, but it is light until 9-10pm around the time your here, so could be a late one.

The changing of the guard at Windsor castle is very nicely done. We liked it better than the big one at Buckingham Palace. After that, you can tour the palace itself, which is REALLY nice.
Windsor is about 3/4 hour by train from Paddington Station. It's well worth the trip.
When we went to the Tower of London, we had lunch at the cafeteria there. It was quite good, and very convenient.

I second Jim's recommendation of the self-serve eatery at the Tower, the New Armouries cafe. I had to wander around for a bit before I could make up my mind. Everything looked delicious. And it was!

My wife and I flew from SFO to London last summer and had such a wonderful time we're going to do it again next summer. I do have a few thoughts on your plans.
The Churchill War Rooms are a must but there is a lot to see there, as they lead right into an extensive exhibit on Churchill himself. You could easily spend hours in there, meaning a later lunch at the Crypt.
We did Greenwich and I was not particularly sold on it either. If you actually want to straddle the meridian -- and, let's be honest, who doesn't -- it is expensive and often involves long waits. That said, the boat ride out is a blast, particularly for kids. You might want to consider adding a Thames tour to your itinerary.
Likewise, there is not a 10- and 12-year-old boy on the planet that will not want to ride the Eye. I'd consider adding it to your schedule -- the kids will never forget the experience.

Throwing some other options for the boys into the mix and reworking your schedule. Parliament Square is a doable, wander, take pictures place so consider this option for Monday. Early departure from accommodation, experience the AM rush on the tube to Westminster station. Exit, Mind the Gap, follow signs to Exit 1. Once outside you'll be face to face where boats depart for Greenwich etc. purchase your tix, then walk across Westminster Bridge to the Eye and ride it just after it opens. Crowds are lite then. After the ride, walk back across the bridge to take pics of Parliament, Big Ben, Westminster Abbey. then into the Abbey and explore. Come out of there and then walk through St James Park, onto and thru Green Park and find the Mark and Spencer. Bit of a stroll but if weather is good, it will rejuvenate you and help with the jet lag. Buy some sandwiches, etc for a picnic. Return to St James park and dine by the lake. Then a walk over to the Churchill War rooms. After that visit and depending on stamina, you could walk up Whitehall to Trafalgar Square and do the brass rubbings at St Martins of the Field. That would be a full day which, of course, could take less time and effort if you bought picnic items the day before and brought with you. I always find that a combination of museums and wandering along the streets and walking in the parks does magic in keeping you awake. Since you are staying in Belieze Park I whole heatedly suggest a visit to Camden Lock Market. Great spot of interest for all ages. Could do that Tuesday after your morning in Greenwich. On Wednesday be at the Tower first thing, go in and head off to see the Jewels first. Then come out see the Ravens and tour where all the armor, swords etc is located. From the Tower walk up the Leadenhall Market. Find the Harry Potter door, to the Leaky Cauldron. Everyone will enjoy it here. Gorgeous glass covered market and a nice spot for lunch. From there to St. Paul's and a climb to the top of the dome. Then if you already have your Wicked tickets, "home" to rest for that nights performance. On your first day and after breakfast why not exploring the Hampstead Heath. very lovely and I'll there's a soccer game or rugby match to watch. Or just enjoy watching people walking their dogs, families out for the day, etc. Then take the tube to the Imperial War Musuem. Continuing....

Part 2 of my reply. Sunday might be the day to experience a pub meal.http://londonist.com/2014/02/20-of-londons-best-sunday-roasts.php

Have a great time with your family!!!

Thanks for all of the suggestions! Too many things to do and not enough time! :)

I was also thinking maybe Hampstead Heath day 1 since it's close and the boys can run around after the long travel...

I think we need to sit down together and prioritize what our favorites are, slot those in as definites. Then we can add a "maybe" to each day, if we have time and energy - but if we miss it it's ok. :)

So many things to do and you all were so helpful! EXCEPT the part about adding MORE things to my list that I want to do! :)

Plus side if we come back when little one does soccer rotation in 2 years from now, I will feel like we could go back to London and have more to see! :)

Thanks!!!