We did a Northwest Arkansas trip so we weren't in Hot Springs very long but we really enjoyed the National Park there. It's in one of the old bathhouses and is essentially a museum about the bathhouse heyday in Hot Springs. We also visited Superior Bathhouse Brewery for food and beer and it was pretty good.
We stayed in one of the historic rooms at the Arlington that still pumped in the Hot Springs water into the tub. The room was outdated and in the middle of summer, had mosquito hawks hanging out at the top of the 10 or 12 foot ceiling but the bath was amazing. It was like soaking in a premade epsom salt bath without the grittiness.
There's lots of cute shops along Bathhouse row, my favorite was an olive oil shop called evil.o (olive backwards) and there is at least one fountain where, if you bring your own container, you can have free water from the hot springs (and it is HOT).
If you have time on your way up or down, we were really enjoyed the zoo in Little Rock too!