Purchase the freshest broccoli you can find. Air circulation will help it stay fresh in your refrigerator or cooler. 1. Remove it from tight packaging. 2. Loosely cover it with a paper towel-lined plastic bag that remains open when stored. 3. Don't let it get wet in a cooler with melted ice. It should keep for 3-5 days at the proper temperature in a cooler or RV refrigerator crisper drawer. See more tips on how to keep camping vegetables fresh.