One night in Cotswolds w/ a 14 year old

Whitsable, Reigate Hill and Gatton Park, Epping Forest. OR train to North Sheen. Exit and walk 4 long blocks to Sheen Road and cross the road at the crossing. Turn left heading towards the Courtland Apartments complex. Walk past them and at Kings Ride Gate Turn right. Signage will say Leading to East Sheen and Richmond Cemetaries. This road/path will take you into the massive Richmond Park. You can hike to the lovely Isabella Plantation of the park. Or walk from the Kings Ride Gate to the New Inn Pub for lunch.

If you’re lucky you may get to see the Red Fallow deer in the park. Richmond is a lovely London neighborhood.

You can't see the Cotswolds via the train. You need to rent a car or take a tour.
Salisbury/Stonehenge are great, and you can take the train to Salisbury, but I don't think Stonehenge has a rail stop.

You can find day tours for Salisbury and probably Stonehenge, not sure if they would be on the same day.

Don't forget Windsor Castle, which does have a train station.

Also, Stratford upon Avon is wonderful, especially if you love Shakespeare.

Canterbury or Windsor would be great visits outside of London. The Cotswolds needs a car as mentioned.

Take the train from Paddington to Moreton-on- Marsh. Bus or taxi to Stow-on the Wold. Wonderful town, lots of easy walks to places like Upper and Lower Slaughter that are the essence of small village Cotswolds.

I agree with the previous poster -- it is possible to see the Cotswolds via train, as long as you're okay with limiting what you see to a smaller geographic area and using taxis or a car service.

There are several places in the Cotswolds with train stations. You just need to choose one with a hotel that you like. And making sure that the town you choose as your base is close enough to get a taxi to a second town is a good idea. From the other poster's description plus a quick look at the map, Moreton-in-Marsh sounds like a great plan.

From Moreton-in-Marsh, it's only 8 miles to Upper Slaughter. From Upper Slaughter, you can walk to Lower Slaughter, then you can continue on to Bourton-on-the-Water (the "Venice of the Cotswolds").

If you don't want to go to the trouble of moving to a different hotel for just a night, there are tons of companies that run tours that will take you to Bath and Stonehenge.

If you did go to The Cotswolds I suggest train from London (Paddington) to Moreton-in-Marsh. Then Pullhams bus 801 to Bourton-on-the-Water where you may wish to stay for the 1 night. (I think it is possible to walk on a footpath from here to Lower Slaughter).
https://bustimes.org/services/801-moreton-in-marsh-bourton-on-the-water-andovers

Have a look at London Walks. www.walks.com

They have re-started some of their day trips outside of London. eg to Cambridge. I can see they have some dates for their Oxford and the Cotswolds walk, but can't see the dates for their walk to just the Cotswolds. But, they are easily contactable by email.
(See they say their Salisbury and Stonehenge walk is still temporarily suspended.)

Several years ago, we did a day trip from London to the Cotswolds. We booked a tour through https://www.tourgems.com/tour-booking.htm and Genny picked us up from Moreton-in-Marsh. We did a full day tour of the Cotswolds and really loved it, but it was a long day. We took the train from London (Paddington Station) to Moreton-in-Marsh and returned the same evening but you could always spend the night. According to her website, she can be flexible with pick up location.

This year, we are planning an all day e-bike tour of the Cotswolds, booked through https://www.cotswoldelectricbiketours.co.uk/tours/. Peter, our guide, will pick us up at the train station in Kingham. Kingham is accessible from London so it’s possible to do the tour as a day trip from London as well. We’ll be staying at the Manor House Hotel in Moreton-in-Marsh and plan to take the train from MIM to Kingham the morning of the tour. Peter does offer other tours but this one worked best for our schedule.

If your 14 yr old is a Harry Potter fan, Tour1 of the Mad Max tours from Bath has some interesting sites, goes to Stonehenge and Avebury, and the Cotswolds. To do this, you would need to spend one night in Bath. My college daughter and I did one of these tours and enjoyed it very much.

Take the train from London to Oxford, then onward to Moreton-In-Marsh, stay the night in a hotel.
The next morning, be picked up by Go Cotswolds tour bus. They will take you to 6 Cotswolds villages and sights, which is about all a person can manage in one day.
The mini-bus seats 16 passengers comfortably, so you are not with a huge bus load of people.

When we were on this tour, we went to Chipping Campden, Bibury, Broadway Tower, Stow-On-The-Wold, Bourton-On-The-Water, and the Rollright Stones, to name a few of the stops. Tom (the company owner and driver) gave out walking maps of each village and made recommendations for shops selling coffee and cakes, and pubs serving a good lunch. Plenty of time was given for us to walk around and take photos at each stop.
https://www.gocotswolds.co.uk/product/cotswolds-in-a-day/

Tom was born and raised in Stratford-Upon-Avon, so he knows the Cotswolds quite well.
Go Cotswolds Tour is highly rated on TripAdvisor, and has just received the Trip Advisor Certificate of Excellence.
You don’t need to rent a car to visit the Cotswolds for just one day. Just contact Tom through his website, and book a day tour. http://www.gocotswolds.co.uk

You will be taken back to Moreton-In-Marsh and dropped at your hotel after the tour. They can drop you at the train station if you wish to return to London that evening.
Another option is to stay on the bus and go to Stratford-Upon-Avon at the end of the day.
(The bus returns to Stratford-Upon-Avon every night.)

If you have checked out of your hotel in M-I-M that morning, you will have your bags with you.
(You can put them under your seat on the Go Cotswolds tour.)
So you could check into a hotel for the second night, in Stratford-Upon-Avon, enjoy being there for part of the next day, then take the train back to London.

On this train ride back to London, you could stop and see Warwick Castle. I don't know any 14-year-old who wouldn't enjoy that. Warwick is one or two train stops from Stratford-Upon-Avon; not far. Then you could hop back on the train to London. The last time I was there, Warwick Castle had luggage storage facilities.

As much as I love London, I'm always happy to have a few nights in the countryside to get away from the traffic and noise for a while.

P.S. If you do the extended outing as I described in my above post, I would be tempted to stop in Oxford on the way back to London and spend the night there. The train line goes through Oxford, from either Stratford-Upon-Avon/Warwick OR from Moreton-In-Marsh.

Lots to do in Oxford. Your family may enjoy a city walking tour from the Tourist Information Centre that includes the colleges.
Oxford is lovely, with great pubs, restaurants and cafes.
Our teen granddaughter loved it when she was there. Of course she's a big Harry Potter fan.
The Thames River runs through Oxford, so you could take some peaceful walks beside the river to relax before returning to the crowds of London.

I believe your 14-year-old will enjoy the train rides very much. Train travel in England is far superior to the Amtrak experience in the USA.