Downtown Delray is genuinely walkable — the central mile of Atlantic Avenue runs from the Intracoastal to the ocean and you can do almost everything on foot. Most visitors park once at one of the public garages (Old School Square garage on NE 1st Avenue is the most central) and walk.
The free Downtown Roundabout trolley runs the length of Atlantic Avenue and out to the beach every 20 minutes or so on a roughly 11am–11pm schedule. Bicycles work well on the mostly-flat streets, and several rental shops are along Atlantic. For longer trips, app cabs (Uber, Lyft) are abundant.