We stayed in Cortona for 3 worthwhile nights, after staying in Lucca for several nights. On a 9 day trip, it sounds like you’re thinking about making a daytrip visit, and not staying the night. If that’s the case, I probably wouldn’t go just for a quickie visit, especially as you’re already seeing Volterra, Rick Steves’ favorite Tuscan hilltown.
If you do want to stay at least one night, Cortona does have its distinctive features. There’s the old town, way, way, way above the separate, newer town way, way, way down below. There are also two train stations in the valley, and we unknowingly got off at the first one (farther from the old town), but still caught a bus to reach our B&B up high. It’s a really steep ride up there, and once inside the old Etruscan walls, it’s a really, really steep climb on foot. On the bus on the steep road back down to the right (closer) train station after our stay, my husband’s 4-wheel spinner suitcase got loose, and sped straight down the aisle of the bus on its wheels, crashing into the dashboard at the front. Nobody hurt, no damage to anything, but really surprising. Hold onto any luggage if you’ve got it with you!