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.
https://www.rome2rio.com/map/Sintra/Albufeira#r/Bus-via-Amoreiras
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.
http://eva-bus.com/
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