Recreational marijuana isn’t legal in NJ yet, but medical marijuana is. Asbury Park’s town government is pro-legalization, but the fate of legal weed will be decided in a statewide voter referendum in 2020.
Decriminalization also hasn’t formally happened yet, although it’s under discussion at the state level.
TLDR; I’m not sure how openly you can smoke weed in Asbury, but it’s a much less conservative town than most.