What airport is best tot fly into?

-Florence (FLR) 1.5 hours away 112.7 km, this airport is smaller, but closer to the town where the wedding is. If you're not renting a car the train station is very close to the airport. Try to take the train to Sinalunga and from there it's a short taxi ride to Montisi

-Rome (FCO) 2.3 hours away 200 km, this airport is large and sometimes the flights are cheaper flying in here. I've never taken the train all the way from Rome before, but I'm sure there are some interesting towns on the way where you could stop for a night and enjoy.

Does Uber or Lyft work in the Montisi area?

It's still not available there. Montisi is a small remote village near other beautiful little towns so they are still catching up to the rest of the world in some ways. If you can, I suggest renting a car while you're exploring Tuscany. There are several beautiful wineries, towns, markets and restaurants to explore. It's much easier to get around with a car.

If you take the train down to Montisi for just the wedding festivities there's plenty to explore near by depending on where you're staying such that you may not need a car.

Coffee shops? Bars? Restaurants? What's available in the small towns?

Montisi, Castelmuzio and Trequanda all have their own coffee shop/bar and at least one good restaurant in each town.