Welcome and congrats on the purchase of your new camper. If you live near Cincy, Ohio, then you have options for a March campout. But the question, how far do you want to travel. Most KOA's are open all winter in Kentucky and Tennessee. In March, the weather will be much more pleasant if follow I-75 South and get about half way through Kentucky and if you go on into Tennessee, you'll have no problems with full hook ups, especially at KOA campgrounds. (I know, we've used several ourselves in Kentucky, Tennessee, North and South Carolina in March (week of March 10) and in December (week of Christmas). We just returned from our Christmas week in South Carolina (Stayed at Santee State Park) for the week. We also stayed at a KOA in North Carolina, along I-40 for an over night and to de-winterize.
March has losts of options, but here again, you'll need to get about 100 miles South of Cincy. State Parks are open too year round, and not very busy at all from November to about mid-April in the Smokey Mountain, Cumberland Gap, Lexington, Kentucky and Knoxville, TN areas. Of course, if you go on to South Carolina, pretty much everything is open in the State.
If all your wanting to do is a couple shake down trips, then your best bet is to do a couple drive-way camps, and if you can't do that because of housing or zoning restrictions, then your next best option is to wait until about 2nd week in April when campground in Indiana and Ohio begin to open up, turn on water, and get things running.
FYI, we go to South Carolina, Georgia, or Northern Florida over the week of March 10. I leave the camper winterized until that trip. I unwinterize once out of Indiana, and leave it that way when returning home (Usually the 2nd-3rd week in March).
Hope this helps.