Key question - which customers do you want to attract? If you aim to take customers away from Dunkin Donuts or Starbucks or McDonalds, you might want different events than if you are trying to pull people away from powdered hot cappucino at the 7-11.
If you start with your business goal, then look at the target audience, the specifics of the events will become much more clear.
Competitive tastings (Pepsi Challenge style) can work and win some PR if you're willing to engage the local media and take a chance that you might not win.
Mug swaps. Bring in any competitor's travel mug in any condition and get a new one from your business with a discount on refills. Make sure you mention this on the mug. You might want a special run of mugs for this even or at least some permanent waterproof stickers.
Raffles work. People always over-estimate their chances of winning and the strange mix of competition and something for nothing will attract people. Just align it with your business and the economics of your business. Trip to Maui might get lots of interest, but you have to want those customers and be able to afford the prize. What is your expected draw, what is your expected retention?
Good luck. let us know what you end up doing.