Reading another question today reminded me of a short story I read in the early 90s (probably written in 60s or 70s though).
"The Wall Around the World", a novelette by Theodore R. Cogswell, first published in Beyond Fantasy Fiction, September 1953, available at the Internet Archive. It has a Wikipedia page.
A society is blocked off by a really high wall; the story follows a girl who tries to get over the wall.
Yes, except that it's a boy:
The Wall that went all the way around the World had always been there, so nobody paid much attention to it—except Porgie.
Porgie was going to find out what was on the other side of it—assuming there was another side—or break his neck trying. He was going on fourteen, an age that tends to view the word impossible as a meaningless term invented by adults for their own peculiar purposes. But he recognized that there were certain practical difficulties involved in scaling a glassy-smooth surface that rose over a thousand feet straight up. That's why he spent a lot of time watching the eagles.
I think she manages it with a hot air balloon.
Actually, he uses a glider aided by a magic broomstick for additional lift:
After checking the broomstick to be sure it was still fastened tightly to the frame, he went swooping down the hill again. This time when he hit the thermal over the clump of trees, he was pushed up a hundred feet before he lost it. He curved through the darkness until he found it again and then circled tightly within it.
Higher he went and higher, higher than any broomstick had ever gone!
When she reaches the other side she meets an older man who had managed to scale the wall in his youth - his solution had been to use a flock of birds to carry him.
Mr. Wickens grinned. Oh, I was born Inside. I went over the Wall for the first time when I was just a little older than you are now."
"In a glider?" asked Porgie.
"No," said the Black Man, his face perfectly sober. "I went out and caught myself a half-dozen eagles."
There might be some magic involved (on the other / better side), or they might just be more advanced technologically.
It's magic (such as flying broomsticks) Inside, machine technology outside:
"Outside, where you're going, is the world of the machines. It's a good world, too. But the men who live there saw a long time ago that they were paying a price for it; that control over Nature meant that the forces of the Mind were neglected, for the machine is a thing of logic and reason, but miracles aren't. Not yet. So they built the Wall and they placed people within it and gave them such books and such laws as would insure development of the Mind. At least they hoped it would work that way—and it did."