Gubbio

You can get there a couple of ways.
1. train to Fossata di Vico (by way of Foligno), then bus to Gubbio.
2. train to Perugia, then bus from the main bus station to Gubbio.

When I was there on a day trip two years ago with Dear Friend two things we especially enjoyed were, first, the mini "train" (actually on wheels), that loaded up on the main piazza up on the "top" and then drove all around historic Gubbio, down to the Roman ruins, and then back up through the historic district. It gave us an over-all look at the town before we started walking around in the heat. The other favorite was riding the "ski lift" thingy up to the top of the town, to the church and restaurants high up, overlooking the town. Do a look on tripadvisor at the actual apparatus. It was beautiful, riding open air over the hilltops, and then delightful having a simple brunch at the cafe just past the church, on the patio overlooking the valley.

If you go up to the church on the ski lift cage (think medieval looking prisoner bird cage), there is one of the Italian skeleton's in bishop robes. A saint I think. Interesting to see, but disconcerting for North Americans who aren't used to seeing the bones of a person on display in a glass case.

Why Gubbio? As you're finding, it's a bit of a pain to get there unless you have a car (in which case it would be about an hour.) There are lots of other wonderful towns much easier to get to from Spello such as Assisi.

If you go to Gubbio (most commonly by driving), then get there early to be able to access the Tourist Information office and the historic palaces, which close for a long lunch period (though churches stay open): http://www.comune.gubbio.pg.it/pagine/main-monuments

The Palazzo Ducale (of the same duke) in Urbino is more impressive (e.g., bigger office of inlaid wood cabinets) but a further drive, also not served by train.