You may want to grab this and hit up the highlights:
https://www.lisboacard.org/
Not sure if it has changed but it is a bit of a pain to pick up. Make sure you have a print out before you go, we did not and they will ONLY accept paper, so we had to hunt for a print shop. Wasted a half a day running around sorting it out.
The Belem tower is neat to see, but busy. Maybe try to time your visit. The Padrão dos Descobrimentos is just down the road. The Jerónimos Monastery is also very near. You take the tram from the main are over here. Be warned, it is a bit confusing, and subject to massive delays. We ended up getting off and walking back after it hit a vehicle. Traffic is horrible in Lisbon, but the metro is great. Unfortunately it doesn't always go where you want.
Ride up to the Castelo de S. Jorge on one of the ricekty street cars, it's a fun experience, then walk down and stop at a cafe on the way back down. The whole plaza area is a bit pushy with people to get you in their restaurants, and it all felt kinda meh. I wouldn't spend a lot of time in the area, but it is where most of the transit gathers.
Staying just outside Albufeira as a base. May be renting a car, haven’t decided yet.
If you want to get away from the crowds and like museums, this is an interesting one:
Museu Calouste Gulbenkian
Where in the Algaarve are you going? Renting a car?