Congratulations! You have figured out the basis of Archimedes' principle. The article linked here gives a satisfactory explanation, though the main point can be made simply:
Consider a vertically-oriented cylinder within the fluid. The difference in pressure between the top and bottom of that cylinder is due to the weight of the fluid within it, and is just that weight divided by its cross-sectional area. Substitute a solid body of the same dimensions, and the difference in the force exerted by the fluid on the top and the bottom of that body -- the upthrust on it -- is the difference in pressure multiplied by the cross-sectional area. But that is just the weight of the fluid that formerly occupied the space taken by that body, and has now been displaced by it.
Considering any irregularly-shaped object as a bundle of thin cylinders, each buoyed by the fluid it displaces, it is clear that shape does not matter, only volume. The upthrust is greater than the body's weight if the body weighs less than the fluid it displaces, and as they are the same volumes, this is just when the body is less dense than the fluid.
The answer to your question, therefore, is that anything of a density equal to or less than than air will float in air, and balloons containing hydrogen or helium are the most common examples. Other answers have suggested vacuum aerogels, but an aerogel containing hydrogen or helium at atmospheric pressure is a more straightforward candidate, as it does not require the gel to have any great strength. For example, the lightest evacuated aerogel achieved so far has a density of 1000 $g/m^3$, and room temperature and pressure hydrogen has a density of 83.2 $g/m^3$, giving a density for the gel, when infused with hydrogen, of no more than 1083.2 $g/m^3$, less that the density of air in the same conditions - 1200 $g/m^3$ (the surface of the aerogel would have to be sealed with a membrane, but its contribution to the density would decrease with increasing volume, by the familiar surface area / volume scaling.)
More radically, this aerographene has an evacuated density of only 160 $g/m^3$.