It was hard for me to think of happiness in Final Fantasy without associating it with something. The first thing that came to mind was the music that plays in Besaid.

After seeing his home destroyed and being slammed around in some Al Bhed ruins, Tidus washes up on Besaid Island. And woah! They have not only Blitzball but some very friendly and welcoming people playing it. He spends moments just floating and contemplating everything that happened. A small reprieve in time from the chaos that had come before and the rough times still ahead.

So it's fair to say there are moments in games I have happy memories of vs generally having a game that makes me the happiest. The trips to Fisherman's Horizon and the Shumi Village stand out, as well.