Sparti has nothing more to offer than probably a day's sightseeing. The town is mostly famous for its history and the glorious past, but today it is just like another small town in Greece: all activities are gathered around the centre, which is busy sometimes but it also has interesting parts. Food is very good in Spartiand there is a paved path with cafeterias and shopping stores. Sparti is the only (I think) town in Greece that has been built with an architectural plan, while other Greek towns usually are a mess, with narrow and complicated streets. All hotels in Sparti is close to the central square, which is very ample and impressive. In any case, every corner of Sparti is no more than 20-30 minutes walk from the centre.
The museum of Sparti is small and exhibits are not well-labelled. A town with such history should really have a bigger museum and the ancient site should get better attention. Only 5 km from Sparti, there is Mystras, an abandoned Byzantine town with a fortress on top and nice churches. About 2 km from Mystras, there is Keadas, the famous gorge where the Spartans would throw their disabled children. The goge is closed today but if you approach, you will feel a cool breeze coming out of it. The good thing is that, even though Sparti itself doesn't have many things to do, it is close to other beautiful destinations in Peloponnese, like Gythio, Monemvasia, Kythira, Elafonissos, Kalamata, so I guess it works like a passage town.