Fira is one of the most picturesque towns I know to just walk around in and you'll find plenty of uniquely Greek things to take pictures of and pose in front of besides one of the best views in the world.
There is plenty of shopping possible including souvenir shops, jewelry stores and arty boutique & clothing stores.
Involved in your explorations will be some climbing up and down wide steps designed with donkeys in mind and thin steps designed for people only. Sensible shoes are always a good idea! High heels are not!!
Money won't be a problem as bank machines are available too.
Visit the Archeology Museum (Tu-Sun 8:30-3, fee), for a collection of geometric red and black vases from the 5th C BC., inscriptions, Minoan ware sculptures, Byzantine art and prehistoric remains. However, many of the best of the ancient finds from Santorini are in the Athens National Archeology Museum.