Many many moons ago, I thought I was going to cut a hole in the top of my butcher block island to make a slot for a garbage access. Well, it never quite worked out.
I think after the PITA of cutting the sinks out, I just withdrew the idea entirely. Not that I wouldn't love to just chop veggies on the butcher block then scrape the excess into a hole with a garbage can attached underneath.... in fact, I may still work on this idea down the road. It's just not a priority.
So in the meantime, for the island, we went to Ikea and bought a clever little plastic bag holder and attached it to the right side of the door under the sink cabinet. On the left side is a roll out garbage can. It's okay, but it's sometimes hard to reach down and pull it out. I just use my foot nowadays.
The other find was at The Container Store. It's a small plastic and wire contraption that holds plastic bags, holds them open, supports the contents, and comes with a lid. We put this right on the door of the main sink, and we're already using it more than the one on the island.
We love it.
I know, I know, "how sad that she gets excited over garbage containers" I can already hear it.
And of course, you'd be right.