I have no specific suggestions, but you should choose your hotel at the same time as thinking about how are you to reach the show.
Hampton Court Palace is at a bit of a traffic pinch at the best times and at the show it is even worse.
The official Park and Ride site is at Apps Court Farm about two or three miles to the west along the A3050 and this counts as Walton-on-Thames so you can try that area, also East/West Molesey. The P+R site is immediately north of Knight Reservoir which shows up on Google Maps. You will see that this site is not in town as such.
Another possibility, is to find somewhere on the local railway line that terminates at Hampton Court station (directly opposite the palace on the other side of the river bridge). Trains from Waterloo every 30 minutes and they usually double the length of the trains during the show. They stop at Thames Ditton, Surbiton, and all other stations (including Wimbledon) to town except Queenstown Road Battersea (but you would hardly want to stay there!!!).
I don't think there is any advantage from catching any coach/express bus from central London as you'll just get caught in traffic!
Kingston is quite nearby too - about two miles. That road will be clogged up, but you could bus it (plenty of buses). It is a busy shopping centre (with shoe shops).
Useful links:-
Train timetable
http://www.southwesttrains.co.uk/uploads/14may10.pdfMap showing bus routes
http://www.tfl.gov.uk/assets/downloads/ ... us-map.pdfSome Kingston accommodation
http://www.smoothhound.co.uk/kingston.htmlSome Walton on Thames accommodation
http://www.smoothhound.co.uk/waltonon.htmlI won't be going to the show, but will be more than happy to see you in the evening.
Ray x