Good timing! I'll be over there in May as well...

My recommendation would still be to skip the AC and distribute those days among Florence, Tuscany and Rome - especially if you plan on returning to Italy. With that said, do some research and see what's right for you and what you two want to do.

Re: a Tuscan base, the Chianti region offers an excellent choice. However, plenty of switchbacks and some deceptively long drives between places. If you're staying in Chianti country I recommend spending each day visiting a new portion of that particular region, as you'll spend a great deal of time getting to say, Lucca, and getting back.

My suggestion, take a look at the Tuscany region in its entirety. You'll notice a diversity of options - Arezzo/Cortona, 'Montalcino area' (includes Montepulciano, Pienza, San Quirico d'Orcia, the Maremma), Chianti (Siena could be included here), west of Florence (so San Miniato, Empoli, Livorno, Lucca, Pisa, Viareggio, maybe Pistoia). There's plenty more area to cover in Tuscany but those are some areas to think about off the bat. See what each has to offer and if that fits into what you want to do. For example, if you're into wine then the Montalcino/Montepulciano/Maremma and Chianti areas will garner greater attention.

As for car options, feel free to use whatever you're comfortable with. I prefer to rent from Maggiore (Italian company) for their prices and fleet availability. Autoslash is a great website to use that will assist in finding the best prices for you.

FYI - More than happy to meet up if you'll be in Florence or the Tuscan region at the same time (looking at May 9-16). Be in Rome on the 17th...