Travelling thru Tuscany in early May without reservations. Doable?

In our constantly-evolving Italy trip coming this May, I'm now playing with the idea of flying into Florence and staying there for 3 nights, and ending up in Venice for 3 nights. In between, I'm thinking about just driving around the Tuscan countryside for about a week, just finding rooms in whatever hill town looks nice as we go, for one or two nights each.

Is that unrealistic? Are most of these towns likely to be fully booked in early May? I'm estimating $250 a night, but we can go a little higher if necessary.