What are some fruits that don't go bad in five seconds?

I go grocery shopping one day per week, on Sundays, and I almost always buy some type of fruit. The only kinds that seem to last the whole week are bananas and apples. The strawberries seem to go bad the fastest and I hate tossing them and wasting money.

What fruits last the longest and what is the best way to store those fruits to keep them fresh? Preferably fruits that are “in season” right now (strawberries this time of year are way too firm and bitter). Also, I only fruit want I can get in your run-of-the-mill grocery store, as I’ve never stepped foot into a health food store and would really rather not.