Just go with Cocos2d. There is certainly not a dearth of Tic-Tac-Toe games in the app store however when I was first learning iOS development I built one of these for a client and it did not take much longer than the two weeks you describe. (Though I had a little help with the art and the Ad integration)
I'd recommend you collect the art and sounds you think you will need from iStock photo ahead of time and I'd push you to leave room for some ads in the app to give yourself an idea of what putting together a complete app that can generate some sandwich money takes. (Or figure out what you could sell via in app purchase) Make it universal if you can as well - anything to get it in more categories on the store. Also go look at existing games that do well to see what they are doing well and poorly. Writing the code is only part of publishing apps and Id say probably not the most important part.
Also, for fun google "Tick Tack Toe in lisp" I found these to be neat little programs to read though not especially relevant to the production of the game :)
You want to release an app or a game? Cocos2D would be your fastest route for an ios game with moving sprites and all that. You don't NECESSARILY need to have all that for a game. You'll lose a half day with provisioning and a half day with submission. Anyhow, there's any level of things in between. You could take an open source game like cloudjump and customize it, or create your own utility.
Look at the Corona SDK for developing iOS and Android apps in Lua. This is fantastic tool. A friend has used this to crank out a number of book apps for iOS using this SDK and the Kwiksher add-on. One note, last time I looked this SDK wasn't using the native UI components, maybe that's changed recently.
Two weeks is plenty of time for a novice iOS developer with a bit of programming experience to publish tic-tac-toe. I think struggling to learn the existing well used tools would be the best use of his two weeks. Try something outside the normal path on the next one once you get something out there.