You could try updating to the latest play store. See AndroidPolice. Doing this fixed the same issue for me when I updated my Nexus 7 to android 4.3. It was crashing like yours, I updated (and cleared the cache and data) and the Play Store started working again. You don't need to be rooted, you can simply install it. It's perfectly safe as it is signed by Google (explained better in the post).
