Staying in Salisbury

The cathedral in Salisbury is probably better than Stonehenge. If you've never seen the Magna Carta, the cathedral has one of the originals.

I would definitely come the day before and stay in Salisbury. Depending on how many nights you are in London, I'dprobably spend 2 nights in Salisbury so you have the afternoon to see Salisbury.

The things I like in Salisbury are:

Salisbury Cathedral
Salisbury Museum - https://salisburymuseum.org.uk/ They have a very good collection of archeological artifacts from Stonehenge. I've seen a couple of really good Constable exhibitions there but it doesn't look like anything is planned for this spring.
St Thomas Church's Doom Painting - This is the small church near the city center that was built for the laborers building the cathedral. There is a wonderful, recently restored, Doom Painting there that is quite unusual.
https://archaeology-travel.com/england/doom-painting-st-thomas-church-salisbury/

I've always wanted to go in to Mompesson House which is a listed building on the Cathedral Close.

I've stayed in several different hotels in the area. My favorite B&B owners retired in December but the hotels were good and there is an old coaching inn I want to try. All of these are within walking distance of the train station:

Rose and Crown - this is the furthest away. I stayed here on a Rick Steves tour. I would not recommend staying on a Friday or Saturday night as it seemed to be a wedding and event venue with parties on until midnight.

Mercure Salisbury White Hart Hotel - I stayed here on a Road Scholar tour. It was fine in 2016 when I was there.

The Red Lion Hotel in Salisbury is the oldest purpose built hotel in the UK (so they say, lol). I want to stay here next time I go.

https://the-redlion.co.uk/?utm_source=gmb&utm_medium=website&utm_campaign=button

We stayed here http://www.qudossalisbury.co.uk/ which is a 10 minute walk from the train station. I really enjoyed Salisbury and thought it was worth a few days. We did the Inner Circle tour and thought it was well worth it to be among the stones. Wear waterproof shoes, the grass was dewy and my wife's feet were soaked. We had a car so transportation wasn't an issue. We also thought the Old Sarum site was interesting and worth an hour or two. I believe there is a bus that will take you there as well.

The Cathedral is well worth a visit. We were supposed to take a tour of the Tower but it was cancelled due to the passing of the Queen. We had a group tour of the town and our guide says the tower tour is the best tour in England.

The museum that Pam, mentioned is interesting as well.

Train to Salisbury. Hour and a half from Waterloo station. Spend the night. Next morning take the Stonehenge tour bus.

The Salisbury Cathedral is gorgeous. Salisbury Museum is fascinating. Interesting architecture throughout Salisbury.

https://www.visitwiltshire.co.uk/salisbury/food-and-drink

This is the Stonehenge Tour bus timetable, in June it will obviously be better.

https://passenger-line-assets.s3.eu-west-1.amazonaws.com/salisburyreds/SWWD/ST-timetable-20220905-9999d23b.pdf

Another recommendation here for lovely Salisbury Cathedral. Definitely go into the cathedral and as Cala mentioned, see the Magna Carta. They have a good lunch cafe in the cathedral with a good selection of sandwiches, salads, baked goods, coffee and teas. Wonderful gift shop with CD's for sale of music as performed in the cathedral. Walk around the blocks near the cathedral. You will want to do as many of the sights as possible mentioned by Pam, above. Claudia gave you great advice about how to take the train from London to Salisbury.
Staying two nights here is a good idea.

Where to go next? Bath is a short train ride from Salisbury, if that interests you.
To spend two nights there before returning to London would be fun.

Arundells, the former home of Prime Minister Ted Heath is well worth a visit in my view. Also.in the Cathedral Close.