Reusable and safe endothermic reaction
There are many endothermic physical processes such as melting ice or sublimation of solid carbon dioxide $\ce{CO2}$. One should also mention thermoelectric cooling effect (Peltier device), which is is rarely effective in practice, yet still an option.

A suitable endothermic chemical reaction would probably be an electrolytic dissociation of certain salts, among which dissolving ammonium nitrate $\ce{NH4NO3}$ in water is probably one of the most well-known and effective examples.