Let's see, there's Missouri Hicks Barbeque in Cuba, always worth a trip, and not hard to find nice roads to get there on.
There's lots of great places for an all-day ride, closer in to town there's some great roads around Highway 94 through the wine country between Hermann, Washington and St. Charles County.
Here's 94 dropping back down from the bluffs:

Ha Ha Tonka is always worth a trip:

although getting to and from the lake is a really long ride on a thumper, especially if you try to avoid the slab.