We depart Heathrow on Saturday, April 26 at 1 PM (13:00). we want to stay in a town maybe a half hour away from the airport, we will be coming from the North York Moors area. Any recommendation of a town and even a hotel . Thank you,

Windsor via train and then catch a bus in the morning

Via public transportation?

Definitely Windsor. If you have a car, from say Pickering to Windsor it will be all on Motorway after Leeds and the drive will take 4.5 to 6 hours depending on traffic on the M1.

Train would be a bit of a pain (especially if you need to drop a car in say York) -- it would be train into London and three changes at various train and tube stations.

Re hotels -- there are many (tons) near LHR at all price ranges. Partly depends on which terminal you are using because they are quite far apart. Just plug your date into Booking.com. For terminals 2 and 3 - there is one hotel right next to T-2 and many along the nearby Bath Road.. Terminal 5 (BA) has the Sofitel attached to the terminal. And Terminal 4 has three hotels with a covered walkway..

we do fly out of terminal 5

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Depending on your budget and using Terminal 5, the Sofitel could not be more convenient. It is attached to the terminal, landside/outside security. There is a Thistle which is near the Pod (sort of bubble tram cars) and a Premier Inn just a bit farther.

If it fite in your budget the Sofitel is by far the most convenient.