<p>I have been thinking about starting a side project at home to exercise my brain a bit.  <a href="http://en.wikipedia.org/wiki/Reversi" rel="nofollow noreferrer">Reversi</a> looks like a simply game, where mobility has a profound effect on game play.
It is at least a  step up from tic tac toe.  This would be a  single player against an AI of some sort.</p>

<p>I am thinking to try this in C++ on a PC.</p>

<p>What issues am I likely to run into?</p>

<p>What graphics library would you recommend?</p>

<p>What questions am I not smart enough to ask myself?</p>

Issues...
Well, just be sure when writing the strategy part of the game, not to simply do the move that gives you the most pieces.  You must also give weight to board position.  For example, given the opportunity to place a piece in a board corner should take priority over any other move (besides winning the game) as that piece can never be turned back over.  And, placing a piece adjacent to a corner spot is just about the worst move you can ever make (if the corner space is open).
Hope this helps!