Happy New Year Wayne,
It is feasible to visit Sintra on a day trip from Albufeira by bus. However, you will have to leave in the early mornings as the trip is around 3 hrs and 53 min to get there. You might want to leave Sintra for last 2 weeks when you have a rental car.
As far as activities to do and day trips near Albufeira for first two weeks, you can use this bus line on link below to plan your trips.
You can then visit these following towns via Bus:
Silve, Lagos, Faro, Vilamoura & Quarteira, and Loule
With Rental Car:
•The pretty resort of Carvoeiro combined with the traditional town of Ferragudo
•The western tip of the Algarve; Sagres and Cabo de Sao Vicente towering cliffs
•The fishing town of Olhao
•Mountain views of Monchique
•Portimao, Praia da Rocha and Alvor