Alright, straight out of the LBI local horse's mouth:
Boat Rentals - This is an excellent way to spend a day on the bay doing some crabbing, and it's affordable. You don't need any licenses or anything like that. Just pay and go - they'll show you how to turn the engine on and steer if you're new at it. You go out with some crab traps and have a great time, then cook your catch at home. It's a good way to avoid another pricey dinner out as well. Try Causeway Boat Rentals right under the Causeway Bridge to the island at Causeway Marina (it's a huge marina, you can see it from the bridge). Tell them Dan from the fishing magazine sent you, they'll know who I am.
Another fishing-related activity is kid's fishing classes run by Oceanside Bait and Tackle. A woman named Val runs the shop and does these classes every summer. It's a wonderful activity for young kids, as they meet at the shop, then go down to the bay beach and learn to fish and crab. They use a seining net to catch all kinds of minnows and small fish, and at the end of the class the kids get to keep a net or crab trap for themselves. The staff does a wonderful job with it. Val is a friend of mine, so definitely mention Dan from the magazine if you go. It's $35 and they run them every Tues and Thurs.
http://www.oceansidebt.com/
There's also a new attraction right in Beach Haven... It's a "pirate ship" type boat that does sightseeing around the island. If you walk down Centre Street in Beach Haven to the dock at the end, it should be there. Capt. Frank Camarda runs it, as well as the Miss Beach Haven party fishing boat, which is another excellent option for a day of fun. If you want to go fishing, they have 4-hour ocean and bay trips. They give you the rods, bait, etc. and the mates are great with kids. Again, throw my name in there. (Damn, didn't realize how well known I was before this post... haha.)
As for restaurants, here are a few of my personal favorites:
Roberto's - Great Italian restaurant in Long Beach Twp., just a few minutes north of Beach Haven. It's one of our family's favorites, even though it's not as well known as some of the others. Not cheap, not overly expensive. BYOB.
Cafe Aletta - Excellent, excellent Italian and Mediterranean food on N. 5th St. and Long Beach Blvd. in Surf City. Everything is a la carte, though, so it can get a little pricey depending on what you order, but most portions are large. It's BYOB as well.
Tucker's - Right in Beach Haven, good variety of food all around, it's not overly fancy but that can be a good thing! It has a bar, too.
Dutchman's - As someone else mentioned, it's on Cedar Bonnet Island (a small island situated under the Causeway bridge) with stunning views of the bay. It's divided between the traditional German restaurant inside and a waterfront tiki bar outside. Cool place. Order a DAB German beer on tap - I always do!
M&M's Seafood: Wooden tables, ultra-casual, open-air. It's essentially a fish market with tables, but the food is really fresh and very, very good. Not particularly expensive. Right on the Boulevard in Beach Haven.
Aaaaaand, finally:
The greatest seafood restaurant at which you will ever eat - but be prepared to drive 20 minutes. "The Octopus's Garden" over the bridge on the mainland on Rt. 9 South in Mayetta. It takes a little bit to get there from Beach Haven but it is an amazing restaurant. The food is out of this world. BYOB, dinners are about $25 or so. Reservations are a must. It's well-worth the drive from Beach Haven.
ALSO:
Great for kids - check out The Show Place. Shore tradition, yes, but keeps up with the times. It's the famous "singing ice cream" parlour. Worth a trip.