Physicist and aerospace engineer Robert L. Forward was credited by Larry Niven with calculating the parameters that would allow a habitable gas torus to be stable in the short term (which in astronomic terms would be sufficiently long), and this was the setting of The Smoke Ring.
The gas torus is made up of a very large (about 9/10th if memory serves) volume where the pressure is gradually increasing and a central torus, still hundreds of kilometers across, where the pressure is suitable to human life.
Within this area, there is no real gravity except for tidal forces, and those only on large floating vegetable life-forms called integral trees. This volume (many times the habitable volume of Earth) seems to fit your requirements.
We can get a different, and still "natural" scenario by using a water moon. Provided that there's some way of keeping it liquid and preventing it from dissipating in space, of course; much the same problem as the Smoke Ring.
The moon itself would have a gravity and would collapse in a spherical surface, and it might have enough floating impurities to form a "peel" reducing water loss (they would also stop sunlight, not that much sunlight would get in the depths).
Unfortunately this scenario too is not original - this is from Iain M. Banks' The Algebraist:
I was born in a water moon. Some people, especially its inhabitants,
called it a planet, but as it was only a little over two hundred
kilometres in diameter, 'moon' seems the more accurate term. The moon
was made entirely of water [...]
If it had been much bigger the moon would have had a core of ice, for
water, though supposedly incompressible, is not entirely so, and will
change under extremes of pressure to become ice. (If you are used to
living on a planet where ice floats on the surface of water, this
seems odd and even wrong, but nevertheless it is the case.) The moon
was not quite of a size for an ice core to form, and therefore one
could, if one was sufficiently hardy, and adequately proof against the
water pressure, make one's way down, through the increasing weight of
water above, to the very centre of the moon.
Where a strange thing happened.
For here, at the very centre of this watery globe, there seemed to be
no gravity. There was colossal pressure, certainly, pressing in from
every side, but one was in effect weightless (on the outside of a
planet, moon or other body, watery or not, one is always being pulled
towards its centre; once at its centre one is being pulled equally in
I once read a fragment of fan-fiction possibly inspired by the Heechee's black hole refuge, where an ancient but reclusive K-2 race was able to create a hollowed out environment at the center of its home star. Then they artificially slowed down the star's reactions to ensure that it would live enormously longer than normal; finally, they settled its core, protected from the Universe by several hundred thousand kilometers of incandescent gases and intending to see their civilization last for some billion years.
In the core, again you would have no gravity; hollow stars definitely are not natural, though. But if the original civilization built sturdily enough, and yet died of boredom some million years later, leaving behind a self-sustaining environment where evolution could have a chance [which requires environment changes and/or a careful setup], that would allow for another race to appear, unaware of living in an artificial environment.