For starting discussions...

The books all below offer "thought experiments", puzzles and short stories that would be useful for starting off Philosophy Café discussions:

Julian Baggini The Pig That Wants to be Eaten: And Ninety-nine Other Thought Experiments
The editor and co-founder of The Philosophers' Magazine “presents 100 thought experiments: short scenarios which pose a problem in a vivid and concrete way, and invites the reader to think about possible answers for him/herself. Experiments cover identity, religion, art, ethics, language, knowledge and many more. From "Zeno's Paradox" to "Groundhog Day" (how do you make sense of a life of eternal recurrence?), via "The Pig that Wants to be Eaten" (so should you eat him?), "Plato's Cave", "Minority Report" (is it right to punish people for what they are going to do, but haven't yet done?), and an "American Werewolf in London" (how can we tell whether we are awake or dreaming?), this book makes philosophy not only mind-stretching but also entertaining.”
You can see some of the country's leading thinkers putting four of the problems under the mental microscope in The Guardian here  and you can search inside or buy it here.

Peter Cave What's Wrong with Eating People?
”With the aid of tall stories, jokes, common sense and bizarre insights, Cave tackles some of life’s most important questions and introduces the puzzles that will keep you pondering throughout the night…  a smorgasbord, ranging from logic to ethics, art to politics to religion.

See a flyer here and buy it here. See also his Can a Robot be Human?: 33 Perplexing Philosophy Puzzles here.


Martin Cohen's 101 Philosophy Problems
”Does Farmer Field really know his prize cow, Daisy, is in the field? When is an unexpected exam not wholly unexpected? Are all bachelors (really) unmarried? Martin Cohen's bestselling 101 Philosophy Problems is a witty and engaging introduction to philosophy, covering classical as well as contemporary problems from the fields of medical ethics, modern physics and artificial intelligence.

You can read the first page, read inside, or buy it here. See also his 101 Ethical Dilemmas here.