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If you ask me, it really doesn't matter which airport you fly in and out of. Its the hotel that makes the difference. Don't even think about public transportation. You WILL need a car so pick up and drop off at the airport would be best. Its an hour (maybe more depending on the time of day) from both airport to Long Beach no matter how you look at it unless you travel after 9pm. Find a nice place to stay for the couple days you are here and enjoy. I know it is hectic but the beach cities are very nice, but can get a bit crowded depending on the time of day or week. A nice meal by the ocean is very nice during spring time. We drive out there often just to hang out for dinner with my family. Long beach's Golden Shore is a nice place to have a meal, take a slow walk and burn a couple hours and enjoy the sunset. LIke Copper said, the "Fish tank " is a nice place to visit with kids even for adults. I suggest you stay out and away from downtown Long beach or the northern part of long beach but down the road, Belmont shore is a great place to people watch, have a meal, but gets crowded during the weekends. I know this isn't a vacation, but after the doc's visit, you will have down time and need to entertain your kid. I wish you the best of luck. There's a lot to do here.