Budget on accommodations?

Well we would like to keep it at $200 per night or less but are willing to go over that also if we really like the place

Yes - sorry I did miss the point about ga9497 (er..what's your name?) preferring to stay in one place for several nights. Personally I think it's fun to keep moving despite the slight inconvenience of unpacking.

Anyway I would recommend

5 nights London
3 nights Bath
4 nights Cotswolds
3 nights York

The castle that was used in the Harry Potter films is in a town called Alnwick (pronounced Annick), on the north east coast of England. It's a popular destination for families with kids who need their Harry Potter fix.

http://www.alnwickcastle.com/ (see the Film Location section)

But Alnwick is quite a ways from anything else, and was used only for long-range exterior shots, and most of those were heavily digitally enhanced (e.g., quidditch games).

Much more practical is a tour of King's Cross Station (where Platform 4 played the role of Platform 9), the Reptile House of the London Zoo, and Oxford, where several interiors (Bodleian Library etc.) were used for the Hogwarts library, hospital, etc. Closeup exterior shots were done at Gloucester and Lacock Abbey. Here's a list for you:
http://us.imdb.com/Locations?0241527

My kids claim that roaming about the stairs and turrets of Warwick Castle was actually the closest thing to feeling they were at Hogwarts.

You could tie one neat knot by taking the train to York from Harry's Kings Cross station -- it's a fast train trip. I was amazed to learn that some folks even commute from there to London (though I can't imagine how much that must cost!)

We loved York when we visited our daughter, who was studying at York University. Interesting city with lots to see (Betty's Tea Rooms, too!), and beautiful surrounding countryside. Good suggestion to train to York and rent a car there.

Planning is half the fun!