I will weigh in with opinions about destinations and time to spend versus trying to create a new itinerary.
Stuttgart: Yes, the ugly stepchild of German capital cities, Stuttgart actually has two of Germany's most beautiful squares - right next to each other. Aside from the central sites, which can easily be seen in a half-day (or less, if you skip the very good Landesmuseum and the Kunstmuseum), the real reason to visit is the Mercedes Museum which is fantastic and I say this as someone who doesn't care about cars at all (but my husband, who very much does, also thinks it's the best of Germany's car museums). Another unique and worthwhile reason to visit is the distinct Swabian wine culture, vis a vis hiking the vineyards and visiting "Besenwirtschaften" - all possible within city limits with easy transit connections.
You don't say what time of year you're visiting, but my recommendation for Stuttgart as a day trip from another place, or a quick overnight would change if one of the better festivals are in on -and there are many, and they are some of the best in Germany. Sommerfest, Weindorf, Fruehlingsfest, JazzOpen, Volksfest, and the Weihnachtsmarkt transform the city into a 2 night stay, easily.
Tuebingen: Worth an afternoon. It's lovely, but it's compact, it doesn't have many good restaurants, and is best thought of as a stopover for a few hours when visiting Hohenzollern than as a destination. If you want to stay in a half-timbered city in the area, Esslingen would be my pick, and it's also extremely close to Stuttgart (and the Mercedes museum is en route from Esslingen to Stuttgart). Esslingen is one of those undiscovered destinations that makes a great base for exploring the greater Stuttgart area with lots to offer on it's own and it's a shame that it's so overlooked. I enjoy Bietigheim-Bissingen and far more Waiblingen as modest day trips from Stuttgart, but Esslingen provides the best experience for a real medieval city in my book and is more convenient to regional sights than the other two.
Freiburg is nice and worth a night, but if I had my druthers I'd base in Colmar. Yes, it's touristy, but it's also gorgeous and is a good base for exploring other Alastian wine towns, which is very worthwhile. I've overnighted in Colmar twice and I'd do it again. Although I think this forum also seems to unfairly dislike Strasbourg, which is just a big beautiful version of Colmar with the added benefit of being a real city with one of the world's most magnificent churches. It is bustling and busy, which I guess some people don't like, but then again, Colmar is just small and bustling so you're not escaping crowds either way.
Stuttgart airport: I hate connecting in the US so I fly from Frankfurt direct to SFO when I visit home, but I will say that for sheer ease of an airport experience, Stuttgart Flughafen is wonderful. I've never waited in security more than 10 minutes through now dozens and dozens of flights. The S-Bahn provides good, regular service to the airport and the station is literally at the airport. I usually arrive at the airport less than 45 minutes before my flight gate closes and I always have 20+ minutes to spare (but then again, I'm not checking luggage).
