Daytona Beach has two calendars. The "off" calendar is shaped by Florida weather: dry, mild winters in the 60s and 70s, warm springs and falls, and hot, thunderstorm-prone summers when temperatures reach the low 90s with high humidity. The Atlantic is warm enough for swimming from May through October. Hurricane season runs June to November but direct hits on Daytona are uncommon.
The "event" calendar is what really determines when to visit. The Daytona 500 in mid-February brings 200,000 NASCAR fans; Bike Week in early March and Biketoberfest in mid-October each bring around half a million motorcyclists; March is also peak spring break, when colleges across the eastern US descend on the beach. During these weeks hotel prices triple, restaurants are slammed, and the beachside is loud and lively — perfect if that's what you want, uncomfortable otherwise.
For a quieter visit aim for late April through May, or September to early October. The weather is still warm, the beach is still wide and open, and prices are at their lowest.