There are a few timeshares in Villamoura (4 Seasons, HGV Villa de Golf (II?, DEX), also HGVC Villamoura (but won't get this via RCI. Difficult to get with HGVC) but can stay with Hilton Honor points because most of it is hotel.
From Villamoura, they can drive (day trip) to Sagres in 1 hour 15 minutes, and Lagos in 40 minutes - good roads. We made a long day trip of this from Villamoura. They will need a rental car.
Lisbon is about 4 hour drive away or a short flight from Faro to Lisbon and AFAIK no timeshares there. That should be a different leg of their trip. Recommend they should also drive from LIsbon and stay in Porto up north in a Hilton or Marriott on points if possible. Porto is a UNESCO heritage site.
Portugal also has inexpensive govt backed places to stay (I cannot remember the name. We heard good things but didn't stay in them) if hotels are not possible.