Departing cl D airport, but remaining within/around its airspace?

What would I say if I just wanted to fly around my local airport, no more than 10 or so miles away. I would normally just say "north departure" in my initial ground call, but since there is a nearby cl C airport to the north, tower usually just hands any northbound aircraft to them immediately after takeoff. In this case, is there something else I could say, such as local flight?