The historic district is small and easily walked from end to end. Parking in the old town is metered in summer and can be tight on weekends; the town runs a free shuttle in season between the main parking lots, the beach, and Cape Henlopen.
The Junction & Breakwater Trail is a paved rail-trail running about six miles between Lewes and Rehoboth Beach. It is the best way to get between the two towns under your own power, and the surface is also fine for jogging or for a quiet ride to dinner. Bike rentals are easy to find on Second Street.
A car is useful if you plan to use Cape Henlopen heavily or explore the inland Sussex County back roads, but you do not strictly need one if you are basing yourself in the historic district.