Alcohol or Dry Wedding?

I am debating whether or not to have alcohol at our reception. At first I was planning an evening with an open bar, then an early afternoon with champagne and maybe one signature drink. But the more I think about it, we don't have any super big drinkers in our family, it's at like 2 in the afternoon. And I'm terrified I'll put down a ton of money for bar tending, security, and alcohol that no one will drink. I can think of other things I'd rather spend that money on, but I don't want to seem cheap and I don't think I've ever been to a dry wedding before. Help!