Falling. Falling towards a planet, star, or galactic core is all pretty much the same. Tidal forces will be a bit different, but those aren't on a feelable scale with most objects.
OK, but as a poor earthling who's never experienced low gravity... surely the force of gravity affects the feeling of "falling" even if you're not in an orbit around some nearby planet sized thing? Does that feel substantially different than, say, falling down an elevator shaft on earth?
"the feeling of falling" -- That's called weightlessness, free-fall, and zero-gee. Being in interplanetary space, being in earth orbit, being in the parabolic Vomit Comet, being in a drop tower capsule, being in an elevator compartment falling down a shaft, stepping off a diving board, there's no difference in the 'feeling'.
The opposite of falling is accelerating, and you feel acceleration. A rocket rocketing in an empty universe would feel the same as a rocket rocketing in orbit would feel the same as a rocket just sitting around on Earth. Wait, that last one's different...
We happen to live most of lives in a somewhat exceptional case of constant acceleration (with respect to falling). The ground below our feet has gotten us pretty used to acceleration. But, if you jump, you'll feel like falling too!