Other possible solvents and their disadvantages;
Water: It's not a good solvent for aspirin, only about 1g/100g.
Other alcohols: None of them are as good or as cheap as ethanol. If you go to
THIS site, scroll down to the results and discussion section and then click on Table 1 of the Thermodynamics of Solvation results you can see the varying solubility of aspirin in methanol, ethanol...through to octanol. Ethanol wins.
Other Organic Solvents: DMSO, ether, chloroform, etc are all harder and more expensive to get than ethanol and a lot of them have special handling and use restrictions. Any of the three above can be nasty if you treat them the wrong way.
Hope that helps.