There are a number of gymnastics programs in Virginia Beach. Parks and Rec offers 6 week classes at these gyms. You have to pay the annual fee, which is about $55.00, then the gymnastics fee. It is sort of a try it out program to see if your daughter likes it. I think Excalibur is in the Kempsville area. My daughter is in the Ocean Tumblers program. She's not very good, but she enjoys the class. They charge a registration fee of $32.00 per year, and classes are $50 per month. Ocean Tumblers has a gym in Chesapeake. All of the programs are about the same price, I think. You just have to decide what you can afford.
By the way, some preschools offer 2 year old programs, or some churches offer Mom's Day Out if she wants to spend time with other children. I know that is hard to find playmates because so many young children are in day care all day, or are holed up in their houses with video games and TV that you don't even know they are in your neighborhood. That's why my daughter started going to preschool when she was two, so she could have socialization