Your best bet for getting into old town Todi (inside the ancient city walls) is to park in one of the parking lots outside the city walls and walk into the town. There is limited parking inside the city walls. Unless you are going into Todi in the very early morning hours, you'll probably find all the parking spots in the very small lots already occupied.
We parked in the lot just to the west of Todi and took the ascensore (funicular) up the hill. This gave us a wonderful view of the countryside and Valle neighborhood of Todi, where the monastery and many residences are located.
From Todi, we wanted to visit Florence, but we didn't want to make the 4 hour roundtrip drive, nor did we want to hassle with parking in Florence. Instead of driving to Florence, we drove 30 minutes to Orvieto, and took the Inter-City train from Orvieto to Florence.
The total travel time one way was 2 hours, and it was much nicer than driving. I highly recommend this as a better way to get from Umbria to Florence.
We also could have taken a small train from Todi and switched trains at Perugia to Florence, but we opted for the Orvieto to Florence train because there were more trains. We bought tickets in Orvieto and did not need reservations going northbound, but could have used them going southbound from Florence.
You could also get on the same train going southbound to Rome.
Be prepared -- trains in Italy are often not on time. We had to wait a bit for our trains. This isn't Switzerland or Germany!