How to prioritize 7 days in central/northern Italy?

For 7 days only you can't do all of those locations. It's a very vast area.
It really depends on what you have seen of Italy already and what you like. I'll give you a description of all the areas:
Dolomites: It is one of my favorite areas in Italy and in August will provide much needed relief from the heat. Besides the gorgeous mountains, you can also enjoy the lakes (like Garda or many smaller ones) and hilly wine producing regions (Valpolicella, just north of Verona). Since that area was largely part of the Austro-Hungarian empire until 1919, both food and culture is still very Austrian. Their specialty will be strudel and sausages, rather than pasta. Small town villages will remind you of Bavarian villages and outside Bolzano (Bozen) where there the majority of the population is ethnically Italian, German is the primary language.
Tuscany needs no description. It's the most famous region of Italy in North America. It's very hilly and there are lots of beautiful small villages perched on hill tops, all with a castle on top, a heritage from the feudal period of the middle ages.
Emilia Romagna is famous for their food. The northern half is flat like Illinois, the southern half is hilly and mountaneous. The major towns are in the flat part, along the hills.
The region is largely unknown to the foreign tourist masses. With the exception of the Romagna coastline (Rimini province) which in August is a zoo traditionally overrun by Italian, German and now Russian tourists. The Romagna coast is called the "Divertimentificio d'Italia" (Italy's Entertainment Factory). There are more theme parks and fancy discos than probably anywhere in the world. Some discos and dancing clubs are larger than an average Walmart store and some discos, like the famous Baia Imperiale discotheque in Gabicce, are as grandiose as a theme park. It's a teenager or 20 something paradise in August, but at my age those crowds give me a headache.
Piedmont has mountain landscapes (Alps) and also hilly wine producing regions (Langhe, Roero and Monferrato). Piedmont is also not overrun by the international tourism masses.
Small towns are all over. There are 8,057 municipalities (Communes) in Italy (as of 2 weeks ago), and each has several separate villages (officially called frazioni or localita' of the Commune) within. So in total in Italy there are nearly 70,000 cities, towns and villages. Take your pick.

I agree with Roberto, you can't do what you want to do in such a short amount of time. His descriptions are excellent. I recommend you choose one area and enjoy the smaller cities.

Thanks so much for your advice. We're definitely not trying to see all of the three regions in 7 days. We'd like to pick two out of the three and stick to small towns whenever possible. I think we're pretty decided on (though not definitely) the Dolomites and Tuscany. I guess Piedmont and Emilia-Romana are the two we're trying to decide between. Any further advice?