Go to this website for photos of Long Beach, so you can see things before you get here. There are pictures of the Queen Mary, the Long Beach Aquarium, the Harbor, and just driving around town.
In terms of local info:
1. The Aquabus: this is great fun. It is a water taxi that goes between Belmont Shore (a four-block strip of restaurants and shops), Shoreline Village (a very touristy pier, but cute; lots of souvenir shops and restaurants); the dock near the aquarium (where you can catch the Passport Bus anywhere in downtown for free); and the Queen Mary.
The Aquabus is a great way to see Shoreline Village and the Queen Mary. The fare is around $2 and when you get down to the docks by the aquarium, you will see the schedules posted on poles.
The Passport busses are free downtown are clearly labelled according to where they go. They are the bright purple and red busses. They go up Pine Ave (arts and shopping area), to the aquarium, to the Queen Mary. The red Passport bus goes to Belmont Shore, but once you leave downtown, the fare is $1.10.
The Queen Mary really isn't the greatest attraction, unless you are really into boats. The "Haunted Queen Mary" tour is really cheesy and much too loud and dark for small children. There is also a WW2 Russian sub parked next to it, but that has a separate admission price. I think the Queen Mary would be the most fun if you were staying at the on-board hotel.
The aquarium is not as extensive as the one in Monterey Bay up the coast, but it worth a visit, especially if you have kids along. The seal show and shark tanks are very popular.
Within Long Beach, public transport is very clean and safe, compared to that of Los Angeles. From the downtown central station, you can catch the Blue Line light rail up to Los Angeles, and you can transfer to the new Metro and other light rail lines that will take you to Pasadena, Hollywood, and downtown L.A. Bicycles are welcome on trains/busses, and bike parking exchanges are available (you pick up a bike and return it later or at another station).
Long Beach is a calm, relaxing community that has a small-town feel to it while still having the bustle of the city. Do be aware that this is an area with a history of industrialism, and is the largest port on the West Coast. Part of your ocean view will include oil rigs, container ships, and oil-drilling islands. In my opinion, that is what makes Long Beach affordable, as the elites flock south to Newport or north to Santa Monica. Long Beach remains a working class town by the sea and I think you will find it is a very nice place to visit.
For budget travelers, there is a Trader Joes at 2nd St. and Pacific Coast Highway, and right next door to it is Farm Boy, a fresh vegetable stand.