You mentioned South America. There are some possibilities, but the problem would be: if you are trading for a week, is there enough to do to fill a week in these locations?
There are a few timeshares in Urubamba, Peru. (On Interval, these will show up under "Peru, Machu Picchu," but the timeshares are not in Machu Picchu.) Peru is interesting, and I have visited this area, though I stayed at the Starwood hotel (Tambo del Inka) rather than a timeshare. It's pretty easy to fill 2 days in the Sacred Valley - there's Ollantaytambo, the salt evaporation pools at Maras, and the agricultural site Moray. You would probably need a car, or a tour guide, to get around. The ruins at Pisac would be further (about 1 hour 15 minutes). You'd also want to travel to Aguas Calientes (by train? via hike?), perhaps stay in a hotel there overnight, and then want a full day for Machu Picchu (catch an early bus up to the site), so that might tack on a few more days of things to do. Cusco is further still (nearly 2 hours by car), so you could add that on to your trip as a several day separate stay.
Once in Peru, there are other areas to visit: Arequipa, Colca Canyon, Lake Titicaca, Lima. So if you're adventurous, you could build a several week vacation in Peru around a timeshare stay. My wife and I spent nearly 3 weeks in Peru and we still didn't see everything. We used a South American tour company to help us arrange our sightseeing while I arranged the flights and hotel accommodations.
A second South America possibility is Bariloche. (On Interval, look at Argentina, "Patagonia and Cuyo.") I have never visited this area, so I can't say anything more, but I do recall someone recommending it to me. If I were looking at a stay in Bariloche, I would see if it were possible to build a trip to Argentina around the timeshare week. That might very well include visits to Buenos Aires and Iguazu Falls.