I suggest looking at anything in Ocean Township, Eatontown, or Tinton Falls. They should have a nice selection of apartment complexes that could fit your requirements.

Fair warning- both Monmouth and Ocean counties have areas that are damn near impossible in the summer time. Monmouth generally is easier because there’s no barrier island traffic that makes the main roads bottleneck. Monmouth, in my opinion, has an immaculate selection of parks and trails.

Year-round, Ocean county is a less friendly place in general.