Sparta is where you spend the night if you didn't make it to Mystras during open hours, before that visit the museum and then hi-tail-it outta there.
The food was good in the little platea and the people were nice! The water is mountain spring so drink up!
The problem with ancient Sparta is that modern Sparti is on top of most of it and what is visible is dissapointing. Even the museum is spartan.
The ancient Spartans, as you are probably aware, thought protective city walls were for sissies and didn't build any.
There are a few ruins left over however and a monument to Leonidas the Spartan King who died defending the pass of Thermopyle during the Persian War.