This exercise will give you plot AND character ideas. Pick a place to sit, and just listen to people as they pass by. Sit outside the library, or at the bus stop, or in a coffee shop, or outside the public restroom in a museum.
Catching snippets of conversation-out of context, no less-will tickle your imagination and make ideas start jumping. The human brain can't help but make sense of what it sees and hears, and when you give it incomplete information, it does amazing things! Here are a few to get you started:
"I need to get back to the rats."
"How would you know? You've never been to the space station."
"Arsenic or cyanide?"
Homework: Tune in to some conversation not meant for you. Don't eavesdrop on private conversations, but find a public place and listen carefully. Jot down 5-10 curious remarks.