Siena or Cortona

Just personal opinion but with 3 nights I would stay in Siena. You could always do a day trip to Cortona. I liked Cortona. and actually if I was going to stay somewhere in Tuscany for a few weeks that might be my choice; but with 3 nights and not having been to Siena before I would choose Siena.

I have stayed in Cortona for a week and explored Tuscany from there, including Siena. We absolutely loved Cortona. It was a lovely town and the food was incredible. Siena was a highlight of our visit to Tuscany for sure, but I wouldn't have done it the other way around. I think you can decide based on the size of the city you want to stay in - Siena has more than twice the population of Cortona. Cortona definitely has more of a small town feel to it, which felt more intimate to me (and might be a nice change after Florence). Both are definitely worth a visit though!

Siena. It has more to see and do. Cortona is beautiful so take a day trip to there. The market day in Siena is interesting. I forgot which day it is. Google it.

If you're driving, then either town works well. I've enjoyed staying in both, with Cortona being noticably smaller. Pick the one of greater interest to you. If you're using public transit, then I'd choose Cortona as it's on your way to Assisi and Siena would be a detour. If you stay in Cortona, a day trip to Arezzo is very worthwhile.

We spent a week on Cortona and enjoyed it. But, I would pick Siena which I have visited more. You really can’t go wrong with either choice. The plus for Cortona is that you are near Umbria if you wish to explore that Province.