NJ Backgammon is a fine bg app for iOS too. I know it allows online play now, but not entirely sure how easy it is find a specific person to play. Worth checking out though as it's a solid game single player too.
BGBlitz is good, excellent actually, for serious play -- probably overkill for the OP's wishes right now though.
I use Backgammon NJ on Android which I saw recommended on BGG. I like this a lot, it seems to have all the features I might need. I know there is an Apple version too.