Florence as a home base

Assisi might be a bit far but Florence is definitely a good home base for Pisa and Siena.

It is a great home base if you don't have a car. Siena is an easy hour bus ride away and Pisa (and Lucca) a train ride away. Assisi is in Umbria and we have always driven there so no personal experience on doing that from Florence. Florence itself is so crammed with Renaissance art that it takes many days to explore.

Assisi is 2.5 hours from Firsnze Santa Maria Novella by train, some are direct while others have one change.

You could visit Pisa and Lucca in one daytrip.

Assisi is not really a day trip from anywhere. After you get off the train at the Assisi station, you still have to get up to the old town, either a taxi or wait for a bus.

You can get to other places from Florence: Bologna, Ferrara, San Gimignano . . . lots of beautiful, interesting towns that are reasonably close by bus or train.

If you don't have a car, Florence is the best base for touring Tuscany. Tuscany's capital city is also its public transportation hub, and it also has fast high speed train connections to Rome, Venice, Bologna, and Milan, all of which are within two hours from Florence.

Assisi is served by direct regional trains from Florence, however it's still at least 2.5 hours to get there, and by car wouldn't be much faster, even if you all speed limits (I always do but it still takes me at least two hours). Unless you absolutely must go to Assisi because your doctor ordered it, there are lots of fine quaint towns that are closer to Florence. For example, in order of popularity:
Siena, San Gimignano, Lucca+Pisa (close to each other), Chianti Hills (wine area), Fiesole (above Florence, so very close), Cortona. Also very easily reached by train from Florence, but totally overlooked by American tourists: Arezzo, Pistoia, Bologna, Scarperia.