How do I fix a hole in a counter top?

Can't really fix that unless you redo the counter.

Pat,

One way to fill the space is to patch it using the same basic method as fixing a hole in drywall with a few tweaks. Consider making it an accent area to the counter. Unless the opening is already a perfect square or rectangle, you will need to use something like a framing square to mark out a square around the opening. You will actually be enlarging the opening slightly to remove any rounded corners or if it is a circular hole. Use painters tape to mark off the square area. Trace your cut lines on the painters tape. If the countertop is a laminate material, you are going to want the edges as smooth as possible when you make the cuts. Score the lines you need to cut with a new blade in a utility knife. Cut all the way through the laminate surface with the utility knife. Use a new blade in a jigsaw or a multitool to make the remaining cuts. The tape and scoring will prevent the saw from chipping the laminate. Next, screw a piece of 1/2 inch or 3/4 inch plywood that is slightly larger than the the opening (maybe an extra inch on all sides) to the bottom of the counter covering the opening. Now you will have a square opening as deep as the counter with a plywood bottom. You can fill the opening with tile, a custom cut piece of marble, or some other material you think will look good with the existing countertop. You are going to have to play around with various materials and maybe have to add some shims or cleats to the opening to get the surfaces flush with each other. Use clear caulking, or grout if you are tiling, to fill any gaps around the edges. You could also use the same basic idea to make a lid you could open and use the interior space for storage, but water might get in. You could not put a bottom on the opening and just make a lid and put a laundry basket under it. It wouldn't hurt to call a cabinet/countertop company and see if they have any suggestions. They have probably been faced with similar requests.

I’d be tempted to use a baking sheet across the hole in the counter, show off decorative perfume bottles, canisters.

Glue and screw in some 1X4's boards around the hole on the underside of the counter creating a lip. Cut a rectangle out of plywood the size of the hole and drop it in the hole. Glue and screw it in. You may need two layers of plywood depending on the thickness of the counter. You can cover or paint the countertop.