Self-experimentation is king. Grind down an aspirin tablet to a powder and rub it on the inside of your cheeks. If it irritates the mucous membrane of your cheeks, it will probably irritate the mucuous membrane of your stomach and should be taken with food. Whole fruits are good. Protein-rich meals will acidify your stomach, making it easier for the aspirin to dissolve. Acidic beverages are also good for this. Even carbonated water is acidic enough for that effect to take place. It's important to not have anything salty with the aspirin, as salt temporarily damages the stomach lining. Of course, taking the aspirin together with mucin would be the safest method.