I have not tried doing this with objective C myself. I would probably start with this project:
I cannot point you to a complete example in objective C. It is not trivial, and, in general, it takes a lot of trial-and-error to get something working. I don’t think you are going to find a complete answer to your question without a bit of your own leg work.
Here is the direction I would take:
- Get oauth working with any Twitter endpoint (starting with PlainOAuth)
- Switch to this endpoint to get your tweets: https://api.twitter.com/1.1/search/tweets.json
If you can get that far on your own, come back here and re-ask your question. That part is fairly simple and most likely you will have answered it yourself.
(BTW, very few tweets – maybe 1% – actually have coordinates data.)