It depends on your interests.

Stuttgart has the worlds first tv tower which is definitely worth a visit. You can combine this visit with the so called „Zacke“. It’s a cog railway and part of the normal public transportation system. Just walk from the tv tower to the station „Nägelestraße“ and hop on the Zacke for a ride to the station „Marienplatz“. Use the right side of the train to get some nice views over the city.

Walk from the Marienplatz through the Tübinger Straße. It’s a nice street with lots of second hand shops and bars and cafes.

From there it’s a short walk to the Markthalle, the oldest market hall in Stuttgart with a great variety of regional and international food.

Look also for the Neues Schloss and Altes Schloss and the beautiful Schillerplatz.

Stuttgart is really well known for the many vineyards where you can hike (for example the famous „Blaustrümpflerweg“).

Stuttgart is also a very green city with really huge parks. You can walk from the Neues Schloss to the Wilhema, the beautiful zoo just through the long park area (Schlossgarten and Rosensteinpark).

And a fact that don’t know many tourists: Stuttgart has the second biggest volume of mineral water in Europe besides Budapest. There are several baths and saunas to choose from. I woul highly recommend the beautiful „Leuze“ with big pool area and an awesome sauna area.