Is your trailer going to be suitable for cold weather use? If the tanks and plumbing are exposed, it would not be wise to use it (or at least the water system) in the Ohio area in March. Even if it is, I would generally suggest waiting until somewhat warmer weather before going on a maiden voyage. Then, too, I rather doubt that too many campgrounds in the area would be open in March or early April, and if they are open whether they'd have the water hookups turned on.
The very first trip I'd suggest would be about 25' or so from your house, if that's possible. Camp in your own driveway. Keep tabs on what essential things you need but don't have in the camper, and get them or at least write down a list of items to bring in when you leave. Try out the various systems--heat, electric connection, water fill, water pump, water heater, microwave and fridge, etc. and make sure you generally understand how they work. If you have a sewer cleanout reasonably close to your driveway (which you probably do if you're on municipal sewer), you can dump your holding tanks there.
As far as actual trips, you probably know as well as anyone where you'd like to go and how far you can travel in a day and so forth. Do plan on covering less ground while towing an RV than when driving a car, and allow time to set up and break camp, when figuring your daily distances. Some people don't like to go more than a couple hundred miles or a few hours in a day, and others (particularly with multiple drivers) are willing to go ten or twelve hours before stopping. Once you have a rough idea of how far you're going in a day and a potential route, you can divide it into segments and see what campgrounds or other accommodations are available around your potential stopping points.
For going to Florida, I-77 covers more mountainous terrain (with some non-trivial grades that require a little care, though certainly nothing at all impossible if you have an appropriate setup) while I-75 goes through Atlanta, which can be quite a mess with traffic. I might investigate US27 from Chattanooga to Tallahassee.
I don't know offhand of anything that gives campgrounds within a specific radius of a location, though doubtless something exists. You can use e.g. Google maps to look up "camping near " and similar searches.