The Duck rides are a hoot, depending on weather. The drivers can be hilarious.
I like the Mountain Tower, which lets you see a long ways. Take time to read all the information placards both at the top (outside) and the viewing deck (inside), below the top.
It's neat to just walk the downtown area. Make sure to visit the Fordyce bathhouse which is the National Park Visitors Center on bath house row. You can tour it too, to see how it was set up in it's operational heyday.
Walk into the Arlington Hotel (I actually honeymooned there) and check out their lobby (you can actually lounge around here and eat dinner or buy drinks without being a guest). There are some small retail shops and a restaurant below the Arlington that you can also check out. Al Capone used to stay at the Arlington. We liked the honeymoon suites, as they were large and comfortable, but have stayed there several years afterwards and the regular rooms are kinda cramped/old style.
History of Arlington Resort Hotel & Spa | Hotels in Hot Springs Arkansas
I kinda liked the new Gangster Museum not too far north of the Arlington on the same side of Hwy 7.
There is live horse racing at Oaklawn, but I don't know their schedule.
I've done several things as we had kids and took them there, or just vacationed that I don't feel are really worth the money/time..... but I don't really want to mention those, possibly affecting your visit to them.
Usually when I go there now or in the vicinity, it for the outdoor things like camping or the lake activities (Lake Degray, Lake Hamilton, or Lake Ouachita)
PS. Take or buy some water containers. There are several free public taps in the downtown area, where you can fill them with their excellent water...which is what Hot Springs is all about.