Safe endothermic reaction that gets below freezing?
The reaction of baking soda and citric acid (both are easy to come by and safe) in water does cool the water noticeably. I have tried it multiple times, and while it does not reach freezing, it will reliably reach $6\ ^\circ \mathrm{C}\ \left(43\ ^\circ \mathrm{F}\right)$, which is cold to the touch. 


  Add 4 teaspoons each of sodium bicaronate (baking soda) and citric acid to a cup. Then add the smallest amount of water you can and start stirring!


You can tell a chemical reaction is occurring because a gas is produced:

$$\ce{3NaHCO3 + H3C6H5O7 -&gt; Na3C6H5O7 + 3CO2(g) + 3H2O}$$

But, wait! We want a temperature below freezing! It might seem a little like cheating, but the reaction still works. Carbon dioxide bubbles are still produced, and the temprature gets down to around $-6\ ^\circ \mathrm{C}\ \left(21\ ^\circ \mathrm{F}\right)$.

If you do not have a thermometer, you can prove the second version is colder than the freezing point of water by doing the following:


Get a small, flat piece of wood and dampen the top surface of it.
Do the reaction in a glass, using 4 teaspoons each baking soda and citric acid and replacing the water with crushed ice.
As the temperature drops, the water between the wood and the glass will freeze, freezing the glass to the wood. If you lift the glass, the wood will stick to it.