Long Beach has one of Southern California's best known LGBTQ communities. The most famous area is called Alamito's Beach, where they have not just one, but several rainbowed crosswalks all along the neighborhood on E Broadway. This road is only 5 blocks parallel from the beach, Ocean Blvd! What a lovely area to be in!
(LGB) The airport is right in the center of the town, only 4 miles north of the LGBTQ area. Quickest public way is definitely a car share or taxi, since its so close and rather cheap, but you want another option, take the bus. The metro is a little west of the airport and need a bus to get there, so might as well take one directly into town.
(LAX) Los Angeles International Airport is nearby only 25 miles north. You can take the Metro Blue Line directly from Los Angeles to the downtown Long Beach; 1 hour and 20min ride.
Long Beach offers the Metro Link Blue Line, which only runs through downtown north and south, connecting the Cruise Terminal all the way to Los Angeles. Otherwise, they offer an extensive bus system.