Taranto has a part of the temple preserved and a good museum, if it's not still being renovated.
Lecce should be on the list, and for non-Roman purposes so should Bari and Matera.
The archaeological sites away from the cities can be frustrating to get to if you don't have a car.
Nevertheless, Egnazia, Monte Sannace, Metaponto and Sibari are not to be missed.
I believe Crotone and Locri are worth the trip as well, but I've never been there.
Finally, there's the museum at Reggio.