You've got lots of time and the internet at your fingers. You can save a lot of money booking on your own.
With the present exchange rate, you won't get much, hotel-wise for $200/night. The best hotel in that price range is the Cranley. It's more like a large B&B (without the second B) located on a quiet residential street. The rooms are very nice. The Cranley is about two blocks from a tube entrance. If it's in your budget, the best hotel in London is the Renaissance Chancery Court - absolute luxury! And it's right next to a tube entrance.
Purchase your tube ticket (via the internet) before leaving home. There's a discounted ticket they don't sell in England.
Be sure to catch Mary Poppins on stage in London. It's great!
Have a romantic dinner at Rules.
Have tea at the Ritz (it's so huge that if you book a late time, you can make it dinner)!
Take a 1/2 hour turn on the London Eye, visit the British Museum, the V&A, and the London Museum. See the Tower of London.
You can either fly or eurostar it between London and Paris. BMI has been having some great fares lately and it's faster to fly - besides, if you took the eurostar, there's nothing to see once you enter the chunnel.
If you want to spend a day or two at DLP, there's a shuttle from CDG direct to to
Disneyland.
Absolute tons more to see and do but I'll stop here. Have fun planning!