We were there just a few days ago! As you know, there are, kind of, two parts to HS....the NP and the rest of the town. (You might look at the lake as a "third part".) We stayed at a BandB near the bath houses.
That part of town is kind of interesting. Lots of tourists of all stripes and types, so the stores and restaurants seem to be pretty welcoming. It was fun to talk with folks around the hot and cold running springs.
I'm a big baseball fan but was not familiar with the region's history as a "spring training" center of sorts.