Travel card for trips outside central London?

you Can not use the travel card for any of the three places you mentioned. The travel card is for thr tube and buses within London only. You will need to go to national rail.co.uk and purchase train tickets. The train to Hampton Court leaves from London Waterloo Station with no changes it’s a 36 minute ride. You can leave from Paddington Station to Windsor and to Moreton-in-Marsh (the only Station in the Cotswolds).

I’m sorry, Hampton Court is in Zone 6, so you could use your card if you buy it to cover Zone 6, buy an Oyster card would be better.

If you are using an Oyster Card to get around London, you can use it for Hampton Court Palace.

Going to Waterloo Station to get to Hampton Court may not be the best way depending on where you are staying. An alternative is District Line to Wimbledon and then switch to the train going to Hampton Court. Much easier if staying west of central London.

There are no barriers at Hampton Court station so remember to tap out and in at the machines located on the side of the entrance to the platform.

For the other two use http://www.nationalrail.co.uk to see your options.

Hampton Court is in Zone 6 so you could use a travel card that covers Zones1-6 but unless you are planning on travelling to other places that day just use an Oyster as it will cap it at the Travelcard price.

For a change in pace and to capture a sense of history you could take a boat on the return trip to London. The dock is part of Hampton Court, easy to use, cost is about $20 and the boat has exterior and interior seating.