Manhattan Beach Blvd goes right to the beach. They have a nice pier with a little aquarium at the end. They even have a tank where kids can touch starfish. They have great restaurants there, bike rentals, etc. They might also be having a beach volleyball tournament at one of the beaches while you're there which can be fun to watch.
Los Angeles is really big and rather than spending most of your time trying to get from one place to another, it might be best to find one area and stick to it. If you're going to see the Iowa in San Pedro, there is Cabrillo beach right near there. I have not been to that beach so I can't say what the crowd is like but you can probably get some info from Yelp.
If you're going to be in San Pedro then there is also the USS Victory Lane to see but if you're going to see the Iowa then that might just be too much of the same thing. You might want to look up the Victory Lane though as an alternative to the Iowa. The Iowa is just a self-guided tour with some volunteers positioned along the route to answer questions. The Victory Lane tour includes an air show, a buffet, and you can take a trip down into the bowels of the ship to see the engines. They haven't set up the Iowa to allow you to see the engine room yet.
Ports O' Call village is near the Iowa. It's a bit junky, but lots of places to eat and some shopping. They have a harbor cruise run by Fiesta Harbor Cruises. It's a little over $10/person for a 1-1/2 cruise through San Pedro Harbor. It goes past the Iowa, Pt. Fermin and other places of interest. We go on that boat ride every year in remembrance of my father whose ashes we dispersed at sea.
If you go see the Iowa the best places for lunch are at the west end or west of Ports O' Call village. Ports O' Call Restaurant and 22nd Street Landing are both great places but a little pricey. Acupulco Mexican Restaurant is good and more reasonable. The Grinder on Harbor Blvd is basically a diner that's a step or two up from a Denny's and might have a better selection for kids.
San Pedro is at the end of the 110 freeway. You can go up the 110 to downtown LA. There you can go to Exposition Park where they have the California Science Center, the Natural History Museum, one of the Space Shuttles, rose garden, etc. all conveniently located in one spot. They have plenty of parking too, so you just have to park once and can spend an entire day seeing lots of stuff including an IMAX film or two if you want.
Another possibility is the set of museums on Wishire Blvd. near Fairfax Blvd. Park once and see the LA County Art museum which has Metropolis II (huge set of tracks with miniature cars running through a maze of erector set buildings. Very cool.), the La Brea Tar Pits, and the Petersen Automotive Museum. There are plenty of restaurants nearby including a Johnny Rocket's hamburger place inside the Petersen Museum. But you can also head up Fairfax and go to the world famous Grove or have a really good brisket or pastrami sandwich at Canter's Deli.
I hope I've provided some good ideas.
Thank you so much! Definitely going to Manhattan Beach.