With my wide angle, I find myself either using somewhat centred shots (and utilising that massive wide angle symmetry) or playing with angles and the corners of the shot. I think part of the trick is reminding yourself that you need to find something interesting while making sure that you're not getting essentially too much in the frame. It's kind of like, finding something to anchor the shot.
Some examples of some of my fav wide angle shots that I've taken to try to illustrate how I like to compose when using my 10-20mm lens:
With this one (ok, my main goal was getting that gorgeous light on the sculpture), but I also wanted to play with putting the focus on the upper left and lower-ish right. It's not centred, and there is more landscape there (like the reflecting clouds), but there's something to anchor the shot.
I pulled this one out because of the idea of ways to photograph a boardwalk / wood walkway sort of situation. Not necessarily something that would work in your location, but my goal was to fill the bottom with the pathway leading the eye down the sidewalk and up into the sky.
Another landscape where I've tried to use the idea of anchoring the shot using something. In this case, it's the cement thing at the front of the shot.
So that's where I'm coming from when I say that it feels like the composition is trying to get everything and needs some sort of focus / anchor.
