I'm in Essex county near the Willowbrook Mall. Same situation - family, kids, limited time to play, want heavy story.
The current 3.5 game I run doesn't have an opening, but in June I'll be running a 4e mini-campaign (or adventure path I think they call it now). It'll be more linear high-action then my continuing campaign which is very RP-intensive, shades of grey sandbox style, but if you're interested I'm always up to meet new gamers. I run one game every other week, during a weeknight.
In addition to the one above, there are a couple of other gaming stores up in my area where you could look for groups. Gamer's Gambit (
http://www.gamersgambitonline.com/) is in Fair Lawn (Bergen County), probably 40-50 minutes from you, but I know they have a lot of groups going, plus a good place to post up looking for a local group. The owners are both people I've gamed steadily with since the '80s.
Time Warp Comics & Games (
http://www.timewarpcomics.com/) is on Route 23 about 3 miles south of where rt 23 and rt 80 cross. Good selection, helpful. They are more of a run-events instead of regular games there, but I haven't been there since my friends bought Gamer's Gambit so things might have changed some. I still recommend it.
Good luck!
Cheers,
=Blue(23)