Tweezers for bee stings is not necessarily a good idea, since squeezing the stinger actually causes more venom to be injected into the tissue, but having tweezers in the first aid kit for other uses is a great idea (e.g. removing splinters). A plain ol' credit/debit card works well enough to remove stingers - simply use it to scrape off the stinger.

I second the cold packs for pain relief...