During the summer months Stratford Upon Avon is always pretty crowded with visitors and tourists.
However it is a fairly large town so it can cope with many people.
One short walk which will take you to the quieter parts is as follows:
Go to the RSC theatre alongside the river.
Then walk towards the church (where Shakespeare is buried)
Go past the church and you come to a small bridge that crosses the river.
Cross over the bridge and you are now on the opposite side from the church.
You are now in the park on the other side of the river.
Walk back along this side of the river through the park (which is a lot quieter than the town side)
You then find yourself at another bridge that can get you back into the town centre.
This is not a long walk, more of a stroll really that will only take about 30 minutes but it is very pleasant.
Note at the end of the walk, before you cross over the bridge back into town, there is a small butterfly farm which is very pleasant. Entrance fee.