buoyancygravity
On Earth, an object less dense than a fluid (e.g. water) would float up to the top surface of the liquid usually against gravity. If there was no gravity, would it still do the same?
Rephrased question: In what direction would an object float in a fluid of uniform density if the object has a lesser density than the fluid?
For completely submerged bodies the buoyance force, being simply equal to the weight of the displaced fluid, is stronger for a denser fluid.
But you know that the buoyancy force for a partially submerged body (like a sailing boat) must be equal to the weight of the body (unless the boat sinks or starts flying like a balloon).
Since the buoyant force is equal to the weight of the displaced fluid, a (non-sinking) boat displaces always the same mass, no matter which fluid, but more volume of a less dense fluid.
A classical example happens if you submerge an egg in water. It sinks to the bottom of the top. Then start adding salt, until eventually the egg will raise. See for example Tommy's webpage:
A quite different question is if a boat would happily float in a denser fluid like mercury, without turning upside down. The shape of the submerged part is very important for the stability. The buoyancy centre must be higher than the centre of mass, otherwise it will be unstable (that is why ballast is needed in many cases, to make a boat heavier in its underwater part... too much of the boat above water would result in a dangerous high centre of mass)
EDIT: Ok, when the partially submerged body is in equilibrium, then $$W_{\text{displaced fluid}}=W_{\text{object}}$$ $$\rho g \Delta V = W_{object}$$
Since $g$ and the weight of the object $W_{\text{object}}$ are fixed, an increase in density means a decrease in the submerged volume, for the equation to hold.
This is because the whole boat, along with the air in the boat, is lighter than the water it displaces.
For example, if a small boat will take up 1 cubic meter of water, then it has to be heavier than the weight of 1 cubic meter of water. This is explained in this post by What If here.
For the same reason that bowling balls float (because salt water the size of a bowling ball weighs more), boats float (because the overall weight of a boat is less than the overall weight of salt water the size of a boat.
Best Answer
No gravity means your liquid would form a sphere, unless you put it in a box.
It would float in whatever direction the forces created by differential heating, or any other turbulence inducing force, sends it in.
Ultimately, if you read about Einstein's work on Brownian Motion, in absolutely calm fluid, it's direction would be decided by the random motions of the molecules of the denser liquid.
This is a simulation of the Brownian motion of a big particle (dust particle) that collides with a large set of smaller particles (molecules of a gas) which move with different velocities in different random directions.