The Galilean thermometers are an example of hydrostatic equilibrium.  If you wish to have one of the indicator balls floating mid-way in the thermometer you may warm the thermometer with your hands for several minutes or use a warm towel until you get it to the desired level.  It has also been reported that a bit of clay can achieve neutral buoyancy in water and is very sensitive to temperature and barometric pressure changes.

Fill the tall glass cylinder 1/2 way with saturated salt water solution.  Then tilt the cylinder and gently pour pure or tap water into the cylinder until it is several inches from the top.  Some mixing will take place at the salt water/pure water interface, but if you are gentle enough this mixing will not reach all the way to the bottom, thus preserving a layer of saturated salt water.  Drop in one or even two hard boiled eggs.

The Three Helium Balloons demo.

One balloon is more dense than air and sinks (blow this one up with your breath or use CO2 to inflate.  One balloon full of helium is lighter than air and will float upward.  The third balloon has a mixture of air and helium so that it is neutrally buoyant (it will not sink or rise).

DESCRIPTION Three mylar balloons are filled with different amounts of helium and experience buoyant forces of different magnitudes as a result. The balloon with the most helium experiences a very strong buoyant force and floats up to the ceiling. The balloon with the least helium experiences a very weak buoyant force and sinks to the ground under the force of gravity. The third balloon, however, has exactly the right amount of air and helium for the buoyant force to equal the force of the gravity, and this balloon rests in midair.
SUGGESTED TECHNIQUE
Attach strings to all three balloons so you can tape them to the table.  Untape the string of the balloon with the most helium. Show that the balloon floats up to the ceiling.  Drop the balloon with the least helium off the side of the lecture bench. Show that it falls to the floor.
Hold the third balloon in midair and release it. Show that the balloon floats in hydrostatic equilibrium. Note: a long string will be attached to the stem of this balloon. If the balloon floats down, cut a bit off of the string; if the balloon floats up, tie on an extra piece of string (string and scissors will be provided).