Long Beach Island in NJ has nice beaches and family atmosphere with plenty of good restaurants, amusement areas, mini-golf etc. And typically the rentals there are more geared toward weeklies than some other areas of the shore. Point Pleasant would be a nice choice, although as mclaurie said, I think the rentals are more full season types (we had lots of friends that did this in the college years & 20's). Point Pleasant does have easy train access to go into the city, and many people commute daily from this area so it is possible. I tend to agree that spending 1 week in the city and 1 at the shore will be more enjoyable and more efficient use of your time.

For the week at the shore you'll still need to rent a car, so a day trip to Six Flags Great Adventure amusement park for serious rides wouldn't be too tough. While in the city, no need for rental car so you can save a little $ there.

Good luck & enjoy NY/NJ!

Just to thank people for all their help. I think I have enough information to start making final decisions.
Maybe I can return the favour some day - if anyone fancies researching a visit to Accrington in Lancashire (birthplace of Butch Cassidy as well as steak puddings)or considering Bronte country two places I have been brought up in, I'd be glad to help.

I grew up on LOng Island....
How about somewhere in Long Beach / Lido Beach/ Oceanside/ or Atlantic Beach. These are beach villages/cities along the very most south western shore of LOng Island. That means you don't have to drive EAST, avoiding much of the infamous LONG ISLAND TRAFFIC. There is a train close by takes you to Penn Station (around 34th street in Manhattan) in around an hour. The hotel options aren't as plentiful, but they do exist. Also people rent out their homes in weeks. There are boardwalks in Long Beach/Lido Beach but they don't have the action that NJ boardwalks have..The boardwalks are just that, without the vendors and amusements. Amusement parks on LI are scarce in general. There is a giant water park if you would want to drive out east on Long Island one day around an hour and a half from Atlantic Beach. Six Flags in Jersey is like 2 1/2 hours away. Lido Beach has Jones Beach which is a giant public state beach...beautiful...with an outdoor stadium for big summer concerts by pop bands ..(things the kids will like, and also older stuff),most nights each week in the summer. (called TOMMY HILFIGER THEATER on the web)
If you decide to do Long Island instead of Jersey, email me becuase i have other ideas as well...
vicki

Steve,
As others have said, don't try to commute between the beach and city. You'll wind up spending too much time in transit. Montauk on eastern L.I. is nice. So is the Jersey Shore. If you choose the Jersey Shore, I would suggest, in order: Wildwood, Seaside Heights and Point Pleasant. All three have lots of rides, with Wildwood having the most. Wildwood is the closest to Philadelphia, and if you're spending a week there, I would recommend visiting that city. Also, go to Atlantic City.

Seaside has amusements, but is definitely seedy! I would not stay in this town as some of the above posters mentioned. Point Pleasant is nice, but aren't the rides more kidde rides? The rides on Long Beach Island are also kidde rides. We always took family trips on Long Beach Island in NJ. It is a nice family spot. I understand Wildwood has a great big beach and some rides for teens. I would also spend a week in Manhattan and than a week at the beach. With your teens in mind, I would choose Wildwood. Cape May is a nearby town with all the Victorian homes(day trip) Also, seedy, but interesting Atlantic City is not far away! You could fly home from Philadelphia.