What's the best airport to fly into?

I'm feeling really overwhelmed with planning this trip to Italy. Due to limited funds and limited time off I can't see everything I want to so I've boiled it down to Florence, Pienza, and Positano (10-12 days). But, everything I've seen online says that to fly directly to Florence is not cheap and that Milan and Rome are cheaper but neither are on my list and would require additional travel time and likely more accommodations to stay at.

What airport would you recommend that wouldn't break the bank and require too much extra travel?

Edit: We're flying from East Coast USA. Also, we're no strangers to long travels and have spent 4 hours taking a day trip to other states.