Germany as a home base

Lots to do in Germany without wandering further. I like flying into one city and home from another using a multi-destination search function. One caution: A natural choice would put Berlin at one or other end of the itinerary. But there are few non-stop flights across the Atlantic from the capitol.. Tegel, the main airport, is vastly overworked and the new super-airport is still not finished. No reason not to work the itinerary but be prepared for to make the international connection.

I assume you fly into and out of Stuttgart - so you must return to STR after your 10-day outing?

"some site seeing, mostly older buildings"

You could very likely find time for a visit to Strasbourg (FR) on a loop tour which might also include several nice German destinations with lots of old-world buildings - maybe some towns in the Neckar River Valley (Besigheim, Bad Wimpfen, Heidelberg, Tübingen and Esslingen, for example) and the Black Forest (Gutach, Schiltach, Gengenbach, Haslach, Freiburg for example.) You will find these and other towns named on the German Half-timbered House Route website, a good resource for someone with your interests.

Will you sleep in Stuttgart the entire time or just the first few days?

Stuttgart is know for its heavy traffic. It is called stau-city. A stau is a traffic backup.

Stuttgart has the nearby Mercedes Factory you might wish to see. The city itself is not such a great tourist site on its own.

You can venture out to either the Rhine Valley, the Rhine Falls, Bodensee, Black Forest or to Munich and Bavaria. However, expect heavy traffic.

I would not try to use Stuttgart as a base, better to go to the places you want to see.
Go to Strassbourg, France and stay there, also the Black Forest at Triberg or Titisee. Heidelberg is good for a day, Wurzberg is NE of there and you could take the Romantic Road. It is great, filled with Medieval walled towns.
https://www.romanticroadgermany.com
The first visitors were friends and families of the American soldiers stationed in the large bases in Bavaria and Baden-Württemberg but the idea of the trail from Würzburg to Füssen soon became wildly popular.

"It's not too hard to see the reason for the popularity - despite the modern roots of the idea, the tour combines the historic cities of Würzburg and Augsburg with the three medieval walled towns of Rothenburg ob der Tauber, Dinkelsbühl and Nördlingen, and then finishes off with the tourist highlights of Neuschwanstein Castle and the Alps."

Just checking, but do you know that Germany is about 500 miles high and about 400 miles wide? You are not going to be touring all of Europe on day trips from Stuttgart!

Have you thought about places that interest you? Germany is a very rich destination with a lot of history and variety. You can only see, say, 1/5 of Germany in two weeks.

Don't use Stuttgart as a base, except maybe for some very close regional day trips, like the Neckar Valley, or the Swabian Alb mountains. As others have mentioned, traffic here is horrendous. It will take too long to get out of the area in the morning, then you'll hit the same snarl of traffic coming back at night.

Tip 1: Use the map of official German National Tourist Board to find interesting locations in Germany. You can add interests on click to filter the map for your individual needs.

Tip 2: For driving ensure having a valid driving permission (more than driving license only). When temperatures are still below 7 degrees (rule of thumb) winter tyres are mandatory by law.

Tip 3: By train (e. g. Deutsche Bahn) you will reach a lot of larger desitinations quicker and more relaxed.

Tip 4: As newbie also have a look at 15 essential tips for travels to and in Germany.

Check out the poster Marcopolko on the Tripadvisor Germany forum. He has a zillion recommendations for the Stuttgart area.

PS- Rick Steves' Germany book isn't really the best if you're basing yourself in Stuttgart. In the state of Baden-Württemberg, he really only covers Baden-Baden and the southern Black Forest, and he inexplicably trashes the wonderful city of Heidelberg, for some reason that most of us can't figure out. Baden-Baden really isn't worth your time unless you're in the immediate area anyway, and the southern Black Forest is just outside the range of a daytrip from Stuttgart. In the same amount of time that it would take to reach the more impressive southern sections of the Black Forest (the northern section closer to Stuttgart is rather unremarkable), you can be in the much more stunning Bavarian Alps anyway.

Not Stuttgart. I go there regularly for work; besides the Christmas market, the car museums and the art museum it is thoroughly unispiring and traffic is atrocious.
Colmar, France would be an interesting base for a few days (4-5, not 10!) with a car, allowing for tours of pretty Alsatian villages and forays into Germany (Freiburg) and Switzerland (Basel, good if you are into art museums, less so if not).
I would then opt for a second base, in Germany, for instance Nürnberg, without a car this time. Day trips to Bamberg, Rothenburg o.d. Tauber, possibly Würzburg too are all easy by public transport.