Are you arriving to FLR after a transatlantic flight?
You might be a bit tired and jet lagged to do anything but going straight to Poggibonsi via the easiest way, which is the freeway way.
If once there, you need to kill time before the agriturismo becomes available, you can still probably leave the suitcases there with the landlord and hit the road for a few hours before you can check in. Besides Poggibonsi itself, which in spite of seeming big and modern, has a quaint ancient city center, very near are the following very famous pretty towns that you can visit while you wait for your farmhouse to be ready:
San Gimignano,
Colle Val D'Elsa.
And just a few extra minutes away from Colle you can drive to Monteriggioni. Certaldo is also near, and so is Barberino.
All of the above are within 10-15 min drive from Poggibonsi.
Going to the SuperCoop supermarket at the Centro Commerciale Val D'Elsa (Elsa Valley Shopping Center) would be a nice introduction to some culinary goodies too (and Coop Supermarkets have great prices). Most tourists who visit Italy without a car don't get to see too many large supermarkets and shopping centers, but in your case you'll get to see where Italians actually shop. Lots of Americans who visit Italy without venturing outside the old historical centers think that Italians shop only at farmers' markets and small shops (big box stores aren't allowed in historical centers). But actually real Italian life isn't much different than in America. There are lots of American style malls and supermarkets a bit outside of the ancient city centers and the one in Poggibonsi is a decent size one (actually they have 2 large Coop Supermarkets).