In early July we were party to a large villa booking by friends. The villa was in a little village, Vorno, near to Lucca, not too far from Pisa. However, it was isolated and a rental car was absolutely necessary. Lucca was really a great town to be near for the week and also because of the summer music festival there. It's just big enough to provide diversion but not too big to be a hassle. Flying into Pisa is easy.

We did a day trip to Florence which is about 80 minutes away by car.

The villa itself provided everything you'd consider to be a quintessential Italian experience. Including poor to non existent air conditioning. There was a pool and tennis court. Plenty of hiking in the hills nearby. Friendly staff but not hotel professional quality. However, having a "house" to go home to in the late afternoon was a real treat.

This villa would be considered "luxury" but I don't know why you couldn't work through Airbnb to find something suitable. Or, as you've seen, the numerous websites. But you're going to have to find a compromise because finding a place that offers that villa experience doesn't really happen withing walking distance of towns with anything significant to offer in terms of fun.

Things you will want to consider is how close is the nearest good supermarket, bank, train station, bus etc.