Most people place them on the side of the sink.

The best location is in the prep zone. Where that is in your kitchen, only a measured layout can show.

In the sink cabinet is a great place if your kitchen is small. That is generally a badly used or underused space, and placing them there lets you use other cabinets for storage. Getting a sink that has the drain offset either to the rear or side will make it easy to have the trash located there. In my 30" sink cabinet, I have a 2 can trash pullout, and a second shorter pullout that holds a smaller compost bin and my dishwasher detergent, sponges, flashlight etc. There is also a garbage disposal and the dish detergent reservoir (for the pump on the counter) - room for everything I needed, but no room for just plain clutter!

Mine is at the end of my island so it is in the prep zone but also close to main cleanup sink which is directly across the aisle from it.

I have a smallish L shaped kitchen and plan for a double trash holder in the sink base cabinet - I just haven't get around to installing it:) Many prefer a cabinet next to the sink so they can stand in front of the sink and open the trash cabinet, but I don't have a cabinet on either side of the sink. I have a set of drawers on one side and the dishwasher on the other. I do have a single basin offset drain - short apron Whitehaven apron front sink. Since it is a "short apron" with an offset drain, I have room for standard size doors and trash beneath the sink.

If the person directed to take out the trash is not the person doing the prep or cooking, then the trash/recycle containers should be out of the cook/prep person's way -- perhaps near the door.