Arezzo as a base of Operations

Orvieto and Florence are as little as an hour away by train, and Siena may be workable by bus.

I have no idea what other places are viable as day-trips. What I'd do is use the Deutsche Bahn website as a first stop to vet possible side-trips. If there is no train service, I'd next go to Rome2Rio to check on buses, drilling all the down to find the name of the companies serving the route. It's essential to continue on to the bus websites, because Rome2Rio's data on travel times and fares is just not reliable.

Keep in mind that few buses are on the road on Sundays.

Speaking of Sundays, as of 2015 Arezzo had a major antique market the first Sunday of each month and the preceding Saturday.

Bologna is a very, very good transportation hub. It's a large city, but it has a huge medieval core. You might consider it as well. The historic center is relatively flat, as I recall.

Excellent choice.

Besides Arezzo itself, you are within short distance from the following famous (at least to Italians) small towns:
Cortona
Anghiari
Lucignano
Poppi
Castiglion Fiorentino
Castiglion del Lago
Loro Ciuffenna
Castelfranco Pian di Sco'

Firenze, Siena, Montepulciano, Assisi, Perugia, and many others are also within 45-90 min by public transit

If you want to taste the typical dishes of Arezzo there are several restaurants to choose from, but my favorite is probably "Il Saraceno". Some of my relatives also like others (my family comes originally from the province of Arezzo, my parents 'emigrated' to Florence in the 1950's) but you can start with that one and maybe ask some local person for their favorites.
In Anghiari I like "Il Feudo del Vicario".

Make sure you learn to say ALO' (from the French Alons). It means "Let's go" but also "Come on!". Aretini use it all the time. Use it too, and you'll be treated like a local. Nobody else in Italy uses that term.

I would add Sansepolcro and Citta di Castello to Roberto's list. We are 70ish and have been to Italy about a dozen times. We visited Arezzo last September for the first time and liked it very much. We would enjoy going back and staying longer than the five nights we had on this trip. We liked Il Saraceno, Ciao Vineria (trattoria), La Torre di Gnicche, and a restaurant called Taste. There was also a bruschetta place (top of Via G. Monaco on the west side of the street).

Thank you all so much for your reply. My wife and I love the city of Bologna but have already spent a good deal of time there. Read Grisham's, "The Broker" if you haven't already. The setting is in Bologna. Most of you have confirmed my suspicions about Arezzo as a base of operations and I especially appreciate the language tip from Roberto. The restaurant suggestions are also much appreciated. I love bruschetta so will have to find the restaurant mentioned on Via G. Monaco. The others will move to the top of my list.

I'm thinking that many of the hill towns suggested will only be accessible by l'autobus so thanks for the bus info acraven. Most of the cities suggested for visitation were on our radar but am curious about a couple mentioned by Roberto. Please if you would, tell me a bit about Castiglion Fiorentino, Castiglion del Lago, Loro Ciuffenna and Castelfranco Pian di Sco'. I'm also curious what you liked most about Sansepolcro Janet?

I'm also wondering if anyone has done a private walking tour of Arezzo. Looking for suggestions.

Grazie tutti

Just google those towns and you can find plenty of info on line, also in English. They are all ancient quaint towns. Using Google Image search you can also see plenty of photos. See what you like best. Cortona is the most famous among Americans, because of “Under the Tuscan Sun” and also the University of Georgia campus there.
But, Anghiari, Poppi and Lucignano are also very famous, historic, and a must. I find Loro Ciuffenna particularly charming as well. One of the most beautiful villages in Italy. Many of the aforementioned villages are listed as “most beautiful villages” in the Borghi d’italia Site, which is an excellent resource to find hidden treasures.
http://borghipiubelliditalia.it
Castiglion del Lago is actually in Umbria, just across the border with Tuscany.

I'm an art nut and was following the Piero della Francesca trail, so I "had" to go there! You might enjoy reading Zoe's 2017 forum trip report about visiting Sansepolcro, Anghiari and others.

Thanks Roberto, I wasn't familiar with the Borghi d'Italia site and from what I've seen of it, it looks very promising. I'll definately be adding it to my go-to sites.

And thanks Janet, for the heads up on Zoe's notes. I'll look for them in the forum