Does research count? For hard problems that I'm not sure how to answer I usually start by looking for any existing tool/framework/technique/blog post/paper that has solved a similar problem. I put copy what I find into Evernote, then, when applicable I sketch out a few different flow diagrams / schema diagrams / etc. to get a handle on how the pieces of my solution fit together.

If something is really complex / important / hard to change later, then I'll usually stop after the research phase and allow my unconscious mind to chew away on the solution, most commonly for me the 'Aha moment' comes during my morning workout. When I'm really stuck I re-read all my collected material, search for prior art again and repeat the process. Sometimes time forces me to just start building, although those are the times when I typically end up refactoring later.

I definitely agree that time away from the problem to reflect leads to a better solution, but IMHO you have to have a really great problem statement and good context for the subconscious to do its best work.