Eureka Springs is an excellent destination. Did you know that Arkansas Tourism has a 'motorcycle dedicated' publication? There's just a lot to be said about the Ozarks -- mostly good. One thing, if you're early in the season (when the dogwood's in bloom), the temperature can vary quite a bit from up on the 'bald knobs' to down in the river valley. So, if the weather turns against you, you may find it nicer along the Arkansas River (or near)?Same goes for your Spring trip down and back -- it he weather becomes an issue; it'll be warmer (and greener), usually, along the Missouri River down by St. Joe. It's really not that far -- you should be able to ride most (or all) of the trip in one good long day.
Welcome to Ozarks, you'll want to ride Scenic 7 and the "Pig Trail", for starters -- and there's many others. A place I'd recco: Petit Jean State Park. Enjoy, you're in for a great time.