Short answer, no need to worry about reservations. We stayed there for 5 nights, but the only reservation we made was for our one fancy dinner at La Grotta at the base of the hill. Wandering the town on several different days, we popped into a couple of wineries (don't recall seeing olive oil shops, but I'm sure they're there), shops and restaurants, and even got an impromptu audience with the legendary Cesare, the town's coppersmith, after poking our head into his shop unannounced.
If it's a nice day and you like wine with your view, head over the Fortezza Di Montepulciano, and go into the wine tasting portion. It's self-serve (1-3 € per tasting), and you can sample dozens of local/regional wines and sit outside and take in the views of the valley and the hills in the distance. On a sunny Sunday afternoon in early April, we had the place virtually to ourselves.
On the other side of town, there's a wine bar at La Locanda di San Francesco, which is a great place to go if want to make the most of your limited time with both good food and a wine tasting experience. Luca and his crew can set you up with a flight of local wine along with some snacks, and probably also direct you to local wineries based on your preferences.