Sounds like a good trip you have planned there.
If you intend on visiting the wine regions, Chianti Classico would be best to do from Florence. Fortunately for you the Vino Nobile di Montepulciano region is closer to Perugia than Brunello, and why not discover the Umbrian wine regions a bit, so the Torgiano and Montefalco regions. Both produce beautiful wines as well.
You can try and dumb in at wineries, and a lot will receive you. However, try to have a plan of which ones you would like to visit, because a lot of them are not placed down the main roads so usually you need to go a little out of your way to get to the interesting ones. Bigger wineries will usually have a tasting room where they offer tastings either for free or for a fee (usually if you buy the fee is taken off). If you are looking for a proper tour of the facilities of the winery, usually you need to book in advance - however, you might get lucky and drop in at the right time...
So that's my advice. I wish you guys a great trip and hope for you that the weather holds.