Time-wise, the last week of March and first two weeks of April is a good bet. No guarantees, but those are the best over the years.
Location and where to stay will take a little more info from you. Most newcomers don't realize how big the lake is. You need to decide what part of the lake you are going to, and give us some info about your boat (or if you plan to rent) to get the best recommendations. Lodging ranges from primitive cabins to fairly nice resorts.
Since you posted in the KY forum, I'll assume you are looking at the KY portion of the lake. Check out
Marshall County Accommodations - Hotels and Motels and
Kentucky Lake & Lake Barkley Accommodations for starters.