Is this your first time in Italy? I don't think you have to do the day trip to Cinque Terre, which in mid-June is run over with many visitors and the experience is more of a "check that off the list" rather than enjoying the place.
With only 4 days in Tuscany, you can enjoy sights much closer and relax as well.
Will you have a car at all? How are you planning to get to Montepulciano and around, other than with group tours?
From Montepulciano, you can dedicate a day to roaming around the Val d'Orcia, another day to Arezzo and Cortona, another day to Siena and the last day to Volterra and San Gimignano. See, 4 days gone and we haven't even gotten to Florence, if you've never been.
As for group tours, yes, the majority start from Florence but if you're based in Montepulciano, the important thing is to look for local agencies.
If you're interested in wine tasting tours within Montepulciano, here are a few:
http://tours.discovertuscany.com/en/...ano/d27742-ttd
But if you're looking for a wider variety, then the Strada del Vino for Montepulciano website has many more options. Take a look here:
https://www.stradavinonobile.it/en/tour-activities/
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