Our trip had 2 nights in Bath, 2 nights near Chipping Campden, 2 nights in Inverness (flew from Birmingham), 3 nights in Edinburgh, 2 nights in York, 4 nights in London.
In retrospect, I think we should have done one night in Salisbury and then 2 nights in Bath and skipped the Cotswolds. The Cotswolds were lovely, but not for the trip we were taking (which was more of a tourist visit than a vacation). The Cotswolds are a place to spend 3-4 nights (rather than 2) just chillin'. Great place - we just did it wrong.
Driving in UK - not near as bad as many on this forum warned. My first drive was from LHR to Bath and other than feeling that the roads off the motorway were a bit tight, it was not a problem. On the other hand, we also liked the trains - there were just a few places in which a car was so much more convenient.
Bath (2 nights is about right unless you wanted to attend many Bath Festival events in May): Marlborough House (lodging): VERY satisfied. Great experience and Peter was a warm host. Dinners at Scallop Shell and George Inn were very good. Mayor's Guide Walking Tour - highly recommended. Bizarre Bath Walking Tour is good, but not excellent. Otherwise, we saw the Roman Baths and Bath Abbey. Both well worthwhile. The walk alongside the canal to Bathampton (George Inn for dinner) was enjoyable - seeing the canal boats was a treat.
Cotswolds (2 nights - see note at the beginning - we visited as sight-seers or tourists, not as vacationers and, therefore, didn't really experience the Cotswolds at their best - better to do 3+ nights with little to no agenda). Charingworth Manor (lodging) was very nice and a different experience than the B&Bs we were otherwise staying at. It wasn't in the Rick Steves literature, so this is a new one and I recommend it. It might be a little pricier, but it wasn't bad. Bring your swimsuit if you go there - nice indoor pool. The downside of this old manor house converted to a country inn is that you're outside any of the Cotswold towns and, therefore, can't just walk down to the pub. Still, there is a lounge where you can mingle with the other guests. The staff was attentive, the dinner was excellent, and the breakfasts were enormous. On our way to the Cotswolds we stopped at Stonehenge (we got the first time slot and were first to the stones - 30 minutes later it had hundreds of people - can't recommend the early slot strongly enough). After that, we went to Salisbury Cathedral, and Avebury. I didn't expect to like Stonehenge as much as I did and Salisbury was delightful (should have spent a night there). Avebury didn't do much for us, but to each his own. Chipping Campden was very cute. We did meet the silversmith mentioned in the Rick Steves book and he was extraordinarily gracious and welcoming to his shop. Stow-on-the-Wold felt (and maybe was) bigger. We just had tea/scones for lunch at Old Bakery Team Rooms which was excellent, and the owner charming. We did the walk from Lower Slaughter to Upper Slaughter (the latter cute but very small and nothing but the church open when we got there). It was different than I expected - we were essentially walking though someone's sheepfolds from gate to gate (watch your step!). My wife's favorite was Burton-on-the-Water, but it started raining hard on us and we had to cut it short.
In Part 2 - off to Inverness.