That's manageable. I can recommend a driver from Florence to the vineyard if you're interested.

May is a good month for Florence. Weather's great, and while the tourist traffic is picking up, it's not unbearable. Plan to bring a bottle of wine and a snack up to Piazzale Michelangelo a little before sunset. It's the best view of the city. If you haven't been there, don't google pictures of it to not spoil the surprise

PM me with some general idea of what you like to eat, budget, etc, and I can help you plan some nice meals in Florence.