This is the second time I've written this, my Laptop chucked me out, so I hope I don't forget anything.
The best time to visit is Mid to late May and June, the last few years, these have been our best weather months, especially up here in Scotland. Also, the schools holiday from the end of June to mid August, so most places are a little cheaper and quieter then.
For accommodation, try hostelworld cot com for cheap hostels and hotels, some of which are brand new, and have great facilities such as free wifi ( which you'll find in most places in the UK - Disney take note!!). There are also some great Caravan and/or Camping Parks in beautiful areas with wonderful views or in close proximity to some of our outstanding natural beauty. Try companies such as Haven, Parkdean and Hoseasons holidays, also if you register for their email list, you're bound to get some good off season offers or price reduction coupons. Or you could hire a mobile home! My best tip for accommodation though, especially if you want to do a touring holiday, is the Youth Hostel Association. Membership costs very little and they have some great properties up and down the British Isles for low cost holidays. In Scotland they even have a castle which is now a Youth Hostel - won't that impress the kids back home!!
If your kids are into Harry Potter, one place which is great is the North East of England. There are a few of those caravan parks I've mentioned in the area, and loads of history and castles. Bamburgh, The Holy Island, or Lindisfarne as it's really called, and Alnwick, which is a quaint litlle town with the most beautiful castle. As a child it was always my favourite place to visit, and now as an adult, I love showing it to my boys as it's the place where they filmed for Hogwarts!!!
Back to Scotland though, which is where my heart is. I second the vote for arran - it's spectacular - I love it so much, I named my son after it! They also have a nice Youth Hostel there. For cities, although most tourists, especially those from your side of the pond, head for Edinburgh, please don't forget Glasgow Smiles Better

(see what they did there?). We have the best shopping in Scotland (second in the UK), and some lovely architecture and history. This is the home of Charles Rennie Mackintosh, and entry to Glasgow museums is free to all visitors, we also have a variety of free events all summer long for all the family, which you can find out details about on the Glasgow City Council website.
In fact, all city councils in the UK have websites, which will help you plan visits with details about what's on when etc. I'd also recommend Historic Scotland and The National Trust and I'd also recommend if you plan on doing multiple visits to their properties to buy a membership (also gets you free parking). Also, nearer the time think about buying a spree book dot co dot uk for discount vouchers for many different days out or places to go and money off meal vouchers for restaurants, they are just like the Entertainment book you have in the US.
Whenever you come, and wherever you go, you'll love the UK. I've lived abroad, but came back because it's so great here, and don't forget to Visit Scotland. (another website name - this time for the scottish tourist board.) X