SUA isn't the most photogenic place at the best of times - the parish church and the river are the most interesting bits. Most of the town centre is geared towards day-trippers - souvenir shops, pizza outlets and so on or is otherwise packed with standard highstreet chain stores. And the parking is bloody extortionate during the day.
Street map here:
http://www.stratford-upon-avon.co.uk/soamapl.htm
What is probably the best tea room in the town is on the first floor above one of the grockle shops. I
think it's on the corner of High Street and Bridge Street, but anyway it's the corner just to the south of the wide street with the likes of M&S on.
The most interesting shop in town is Paxton & Whitfield, the specialist cheese place, on Wood Street.
http://www.paxtonandwhitfield.co.uk/
There
is a butterfly farm, but when I went (some years ago now) most of the butterflies were very raggy looking. You could use a tripod though.
Other than that, and going to the theatre, you're best going out of town if you have transport. Warwick has been mentioned. There's also Ely and Pershore and down towards the Cotswolds, eg Stow on the Wold, Broadway (though that's rather touristy as well), Moreton in the Marsh and Chipping Campden.
If you're into art, there's the private art gallery and museum at Compton Verney (excellent restaurant and tea room as well).
http://www.comptonverney.org.uk
Batsford Arboretum at Moreton in the Marsh.
http://www.batsarb.co.uk/