Of course, you have to go check out the various Springs in the area.
Ermilio's is great, they make a helluva martini. The town itself is probably unlike any other place in Arkansas, in that it's pride banners and gay stuff everywhere. That said, it's a blast though. Wife and I went a couple years back and stayed in a tree house cabin in the woods outside the town.
Check out the "all faiths" glass Church, pretty cool. Oh and if you want a seriously freaky visit, check out the Christ of the Ozarks statue and museum...it's very culty to be sure, but it's an oddity worth seeing.
https://en.wikipedia.org/wiki/Christ_of_the_Ozarks
We enjoyed our time in Eureka Springs, though I don't know that we will hurry back. Someday I'm sure we'll go again. It's beautiful for sure.