Stuttgart has an excellent transport network, consisting of trams, buses and trains. The buses and trams spread out pretty well across the city, and the trains, which include the S-bahn (the suburban railway), the U-bahn (the underground) and some mainline routes, are equally efficient. The entire public transport is integrated, and it makes sense to buy a 24-hour ticket that allows you unlimited travel on trams, buses, and trains.
One of the most convenient ways, however, of getting around the city is to hire a car from one of the many rental agencies in town and drive around on your own. Alternatively, you could hire a taxi, by phoning for one, or hiring one at a cab rank.
Unless you’ve got a very sturdy pair of legs, and like walking, don’t attempt to do much sightseeing in Stuttgart on foot - most of the sights are spaced very wide apart.