Brown County State Park in Nashville, IN has both trails and cabins. Problem is, spring is a bad time of year for mtb riding in this part of the country because frequent precipitation and low evaporation means the trails take a long time to dry enough to be rideable. Pavement and dirt/gravel roads are a better option. You will likely get stretches of weather good enough for mtb riding in the springtime, but it will be nearly impossible to plan for them.
Plus, when spring is in full swing, lodging is tough to find in Brown County unless you plan a LONG ways in advance. Last year, I found a month to be insufficient.
If you want to ride at a particular time with less need to consider trail conditions, you'd be better off heading south. Lots of people in Indiana will head to KY, TN, and NC. You may want to consider Arkansas, too.