Quite a few people who hire bikes from me stay for the weekend in a local B&B or hotel and use it as a central base for their cycling. It sure beats lugging your luggage with you all weekend.
There are loads of routes from Stratford heading out in two or three different directions. Distances range from 10miles up to some rather challenging 50mile plus distances. The other advantage is that returning to Stratford each day there are loads of things to do and great places to eat.
I have a list of accommodation in Stratford on my website however there are a couple of places I would recommend. The Alveston Manor is great as they will store your bike for you (as well as being a lovely hotel) and for B&Bs try Ian at Ashgrove House or Tim at Virginia Lodge. Both are close to town and really well run!
If you are interested give me a call!