One of my favorite things to do is find a nature shot where I can use a natural frame for my subject.
The easiest "natural frame" is from plants. I've used an overhanging branch to add emphasis to beach. The top part of the shot would have been a very dull and boring sky but with the overhanging branch, I had a great combination.
I think my favorite frame was a piece of driftwood that had a natural "hole" in it in the shape of an eye. I was able to take a photo of another piece of driftwood that had an interesting look to it with the "eye" of the closer piece serving as a natural frame. With that photo, the further piece of driftwood really wasn't interesting enough on its own, nor was the hole in the closer piece. Together, though, they made for a fabulous photo.
I've used the open porthole of a ferry to frame the city. I have a window framing a different window behind it. I got a shot of the Seattle Space Needle through the opening of a sculpture in a park that overlooks the city.
One of my favorite natural frames belongs to a friend--you have no idea how much I wish I had gotten this one. She had taken her granddaughter to a fast food restaurant that had play equipment. One of them was some kind of structure with round openings in it. My friend's granddaughter sat down right in the center of one, with her legs crossed, and just smiled out at Grandma. Fortunately Grandma had her camera with her. There is absolutely no way she could have created that set-up--children are famous for not cooperating with set up shots. This was just one of those times when a child just happened to sit in the very most perfect place and there was someone with a camera to capture it.
This isn't something that is going to be available everywhere you go, but if you keep an open eye and an open mind, you have a far better chance of finding a great opportunity than if you stick with the obvious.