I just found that I also have this issue. The problem with the green-checked answer is that Alt+J is used for finding the Next Occurrence and it conflicts with that. I use that shortcut a lot when using the Multiple Cursors feature.

And I set Shift+K for showing the pop-over on my code (an equivalent to when you hover on the variables, classes, etc.).

So, I'm going with the Ctrl+N for Down (Next) and Ctrl+P for Up (Previous). I won't need to go left or right in the menus anyway. And, in my experience, I don't use the existing keymaps for Ctrl+N and Ctrl+P. I've never knew about them.

I'm more happy with this choice and don't see a point in going left or right in the tool windows or other menus.

Cheers.