This is a little unusual, I didn't know AI's had "hotel only" options. I'm really surprised about the "a-la-carte" option. It's perfectly normal for AI's to offer "day passes" (complete with food) for non-hotel guests, but the doing it the other way around is sort of, well, contrary to the point of being an AI.
Even if that's the case, are you saying the buffets are NOT included, or that they are, and you're looking for sit-down restaurants?
Worst case, you can do dinner at the AIs (80ppd comes to $560 over the week), and then grab some light fare for brunch. Otherwise, I'd definitely go with whatever suggestions you can get from Chiri and MikeFisher, who are extremely familiar with the area. If you can scrape up an extra hundred bucks or two, it really would go a long way.