R's nest of zombies shambles aimlessly around an abandoned airport day after day after day. It's kind of like that time that dude from Twilight peed all over LAX times a thousand.
The airport is thematically appropriate because it's like a holding cell, a purgatory, between one part of life and another. There is no movement within the airport itself. The zombies are stuck, stagnant. They ride escalators and moving walkways for fun, showing how lazy and apathetic they are. They cannot move themselves; they need machinery to do it for them.
At the end of the novel, R says, "to fix a problem that spans the globe, an airport seems like a good place to start" (3.1.61). But does it really? R's airport has no flights, ever. And you thought delays today were bad. These guys are permanently grounded, and we wonder if they ever will get up in the air again.
A stadium is a symbol of recreation and community. Neither of those things is happening in the stadium where Julie lives. The stadium of the Living is a microcosm of our society... and everything that's wrong with it. After the zombie apocalypse, they planned to rebuild society anew! Glorious change! But it didn't take long before society ended up right back in it's own traps—literally.
Democracy isn't quite working out for starters. "We enthroned the majority and ignored all other voices" (2.2.23), says Julie. It doesn't help that her dad is in charge and has implemented prohibition, which seems like a pretty awful way to go about the apocalypse. Plus, kids are taught valuable survival skills, which is great, at the expense of reading and the arts, which is not. It's all work and no play here, and after slaving all day you can hit the bar... the juice bar.
The stadium shows what happens when we give up freedom for safety. It takes safety measures enacted after 9/11 and takes them to the extreme. Julie says it best when she says, "We think we're surviving in there but we're not" (2.7.229). They may be surviving, but are they living? And which is preferable?