This article includes a great chart that identifies the best storage place for different fruits and vegetables. It also talks about which produce you should store separately to avoid ripening too quickly.
"Are you wasting food because it ripens-then rots-faster than you can eat it? (We're sheepishly raising our hands along with you.) Storing food the right way can make all the difference. Ethylene, a natural gas that's released from some fruits and vegetables, speeds up the ripening process. That can be an advantage-to ripen an avocado quickly, seal it in a paper bag-but too much ethylene can cause produce to spoil. And it's not all about ethylene; temperature plays a role, as does how and when you wash a fruit or vegetable, and how and where it's stored."