Suggestions York, Bath and in between

I would definitely not sleep in Bath the night before a transatlantic flight out of Heathrow. Although a catastrophic transportation problem is unlikely, it will be very costly if it happens--two one-way tickets back home at the walk-up price.

I haven't been to Windsor, but I understand that it is nice, and it's very close to Heathrow. That's a place you could stay your last night and not need to worry.

Not having driven in the UK, I'm going to let others comment on the feasibility of detouring to the Cotswolds and Bath. ViaMichelin.com indicates Bath won't add tremendously to the York-Heathrow driving time, but of course there could be traffic delays, etc. I didn't attempt to map out a Cotswolds loop.

For a suggested interior route back you could check out this fairly direct but not obvious route: York> Hull> Lincoln> Stamford> St Albans , Hull was the Uk Capital of Culture in 2017, not pretty village but interesting all the same. Lincoln has a magnificent Cathedral. Stamford is cute and St Albans is an attractive historic town with some interesting Roman Villa remains and close enough to drive back to Heathrow in a morning.

FWIW, I have a friend in Bristol who will drive to Heathrow on the morning to meet us for a 9:00 flight. Granted, he knows the journey and is confident in making it by the skin of his teeth and he starts early. With this in mind I would be confident in taking the National Express coach from Bath for a 14:15 flight (I'd make it an early one just to alleviate any anxiety).

However, I wouldn't opt for Bath on this occasion as I think there's plenty to see and do in Yorkshire and the surrounding areas. Unless there's a very specific reason for visiting Bath other than it's seemingly on every American tourist's "must see" list then it's a waste of most of a day. Why not rent a cottage for three nights in somewhere like the Yorkshire Dales and spend your remaining days exploring villages, enjoying the scenery, take in the odd pub or two, visit a few castles and ruins and any number of sites looked after by English Heritage: www.english-heritage.org.uk/visit/places/#?page=1&place=yorkshire&mp=false&fe=false

For longish train journeys - such as London Kings Cross to York - you will find cheaper pre booked advance fares for specific trains get loaded around 11 weeks ahead. Play around with www.nationalrail.co.uk and you will see what I mean.

Yorkshire is great, we loved going through the Yorkshire Moors to Whitby. Also, Durham is worth a stop.
Between York and the Cotswolds, Warwick with its castle is another.

We stayed in Chipping Campden, Volunteer Inn is nice with a great pub and Indian restaurant.

Thanks guys! Exactly the kind of advice I was hoping for.

We really enjoyed Durham. We stayed at the Marriott and had a view of the river, which has a nice walking trail. Durham was a nice quiet stop but I don't consider college students to be noisy-they were a nice break from tourists!