This is probably one of the richest areas of the country for things to do, shopping, and dining.
We've done a lot of the things already mentioned. Let me add a couple you might like.
Shopping: Festival Lakes is one of the larger flea markets around. It's all indoors. A lot of junky stuff but there are some pretty good shops as well. Boutique shopping in Fort Lauderdale. Everything in between.
Dining: Great German food at Cypress Nook. Cap's Place near Hillsboro Inlet (
http://www.capsplace.com/). Malulo's International Seafood (Peruvian, on E. Atlantic Blvd, a few blocks west of A1A; totally awesome ceviche). Christina's Greek restaurant, also on E. Atlantic. Our normal place to stay is Wyndham Santa Barbara so my recommendations are closer to there than to Palm-Aire.
Tours: check with the concierge/activities desk at the resort. We've done swamp tours, snorkeling, duck tours, day trips to Miami and Key West. There are lots more available. There are casinos nearby.
And the ocean at Royal Vista will be delightful.
Your week will pass before you know it.