If you are not driving, Perugia is the best choice to base your stay in Umbria. It is the major center and is also the main hub for trains and bus linking the towns of Umbria that worth to visit.
Also, Perugia offers lively night-life as well as good eating and lodging options. In summer you can enjoy excursions to Lake Trasimeno, just a 15 minutes train ride from Perugia.
Another good choice is Assisi. Even tough the train station is a couple of km from the town center, it is well served from an excellent bus service.
Choosing Perugia or Assisi gives you the easiest way to plan trips to the other historic centers of Umbria.
And if you get tired to travel, Assisi and Perugia, offer plenty of sightseeing activities to fill your stay. (See map of Umbria)