First, when you buy your train ticket to Stratford-Upon-Avon, use the full name at the ticket window. There is a Stratford in England, but that's not where you want to go.
Stratford-Upon-Avon is one of our favorite places in England. See the Shakespeare houses, the Royal Shakespeare Theatre by the River Avon. Then walk down to the church where Shakespeare is buried, Trinity Church. The church is several blocks south of the tourist-filled area. After seeing the church, walk west a block or two and around there, to see some old timber-frame houses without the tourist crowds.
There is a canal that runs through town, and there are many narrowboats tthat people live on anchored at the side of the canal and in the "pool" of the River Avon near the Theatre. There are many ducks and swans on the water. A very picturesque and serene place.
I would urge you to spend at least two nights here, or maybe three.
On one of your days, you may want to take a tour through the Cotswolds with Go Cotswold Tours. We took this tour last spring, and it was excellent. See my thread/trip report here:
https://community.ricksteves.com/travel-forum/england/stratford-upon-avon-travel-tour-cotswolds
On one of your days you may want to take the train, bus, or taxi (short ride) to Warwick to see Warwick Castle.
Stratford-Upon-Avon is easily reached by train from London.
If you need restaurant or hotel recommendations, I have some for you.