You can get out of a cylindrical hole by wall-running in an upward spiral.

You can escape a gravity well without propellant, if there's a big crowd of you. Arrange yourselves in a spherical shell around the Earth. Now push away from each other, the shell will expand. Voila, you're going up without using propellant.

How big a crowd do you need? Two people is enough. Push away from each other, and when you meet on the other side of the orbit, push away from each other again and so on. You'll rise higher and higher.

In fact, don't even bother catching the other person. As you pass them, just shove them in the direction they're already going. You'll keep accelerating along opposite orbits until you reach escape velocity. You can even catch each other on the last loop, reclaim the collision portion of the energy with regenerative braking, and fly away together.

This makes the rocket equation irrelevant as long as you're in a gravity well. To get higher and faster you only need a linear amount of energy, not an exponential amount of propellant.

Another option is to have the propellant bounce off the planet. This is easiest if the propellant is photons. Put a corner reflector on Earth and another one on the spaceship. Shine a light and let it bounce back and forth, accelerating the ship. This will work without any gravity well limitation, because the light will always be faster than the ship. (This isn't perpetual motion, because the light will redshift and lose energy with each bounce.)

What if you're trying to fly away from a black hole instead of a planet? Then you only need one reflector on the ship. Shine a light at the image of your ship visible around the edge of the black hole. When it arrives, reflect it back, over and over. The light will keep pushing you up.

This works at any distance from the black hole, too. No matter how far you are, you can always shoot a light beam that will pass near enough the black hole that it curves around relativistically and comes back exactly where you plan to be. If you're patient enough, you can travel the universe by bouncing a bunch of light off various black holes, redirecting and reusing it as you go.

Of course this is all wildly, wildly impractical.

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