Here's a few resources for planning a bike ride (esp. Mountain biking) around Newark, DE.
White Clay Creek trails around Newark, DE - As shown with a general search on RideWithGPS
Pomeroy + Climbing Loop v3 - The Pomeroy trail, starting near Newark Reservoir. A great, simple and "mostly" flat ride. Fantastic for getting started riding for the season, or in your life. Shocks will make it more comfortable, but you can use any bike. If you don't feel like doing the climb when you get to the historic London Tract Church, just turn around.
White Clay Creek Full - A simple and fairly complete loop of White Clay Creek, Middle Run, and Judge Morris Estate
WCC Big Loop - White Clay Creek, Middle Run, the Reservoir, and Judge Morris Estate, including Cart Path/Boundary Line
Unofficial White Clay Creek and Middle Run Map - Ken Cox has done an incredible job.
You may also find helpful info on the Official White Clay Creek map, and note that you can connect to Fair Hill (MD) trails OR White Clay Creek Preserve (PA) trails with a little planning.