I love Monticchiello. It is very close to Pienza. When in Tuscany, we always stay in Cortona and it is not too far from Montichiello. I think it would be a fun day trip. I have been to Assisi twice, but I can't remember how far it is from Cortona. I think it is between 30 minutes to an hour away, so it is doable as a day trip. If you go to Assisi, you should consider hiring Anne Robichaud as a guide, she is fantastic. Her website is at annesitaly.com. If you don't take her tour, or if you do a half day one with her, you might be able to combine Cortona and Assisi in one day.
I love Siena too. You can probably combine Siena and San Gimignano in one day trip.
We have not been to Grosetto or Lucca. If you are interested in wine, you could substitute Montalcino and Montepulciano for those towns. Both of those towns are close to Monticchiello and both are very picturesque.
Be sure and drive some on the "strada bianca" or gravel road around Monticchiello.