The distance from Sandy Hook to Absecon Inlet (Atlantic City) is about 75-80 nautical miles. Certainly do-able in one long day, depending on wind and sea conditions. You'd have to leave very early, though, to get in before dark, since you'd likely be looking at a 10-hour trip or so, given favorable conditions.
HOWEVER, you can't depend on favorable conditions. I've been into both Barnegat Bay and Atlantic City with my boat (6.5' draft) due to unfavorable conditions (wind and seas building from the wrong direction, or storm threatening). Therefore, IMHO, you should:
1. lay the course out on your chart and see for yourself the distances to where you'd have to go; and
2. be prepared, if necessary, to duck into Manasquan, Barnegat, or Absecon Inlets.