Things To Do

I've never been to Portugal but I have googled a bunch! You can use my research as a jumping off point for planning your adventures!
The primary thing to do in Carvoeiro is enjoy the beaches! There's oodles of cool beaches with limestone cliffs. Some have parking lots and trails down to them, others are only accessible by boat or kayak. There's also the Seven Hanging Valleys hike along the top of the cliffs.
There's lots of aquatic activities, including paddle boarding, surfing, boating...
There's plenty of wineries and vineyards in the area to go wine tasting!
The coastal Benagil cave looks awesome and also totally overrun with tourists.
If you need some "city" in your vacation, Portimao is the closest, only about 5mi away. Museums, shopping, more restaurants, etc.
Faro and Lagos would be easy day trips with lots to do. One thing I noted is a creepy chapel made from human bones, Capela de Ossos in Faro.
Lisbon is about a 3 hour drive northwest and has plenty to offer as well!