Hello, Faro is one of those places you should go to there is so much to see, perhaps the best way to get there is by bus, the bus station is right in the town next to the harbour.
There is a old walled town with its Cathedral well worth a look and then go up to the bell tower for some great views of the town, sea and even see the planes coming and going from the airport. There is also a nice museum in the old town and a nice walk round the walls.
There is a small Maritime Museum near the Harbour and then there is a Church with its Chapel of the Bones, The town has lots shops with big names if you need that some thing you may have forgot and plenty of nice cafes for lunch.
If you have a car take a drive over to Tavira a very nice Portuguese town and even go as far as Vila Real on the boarder with Spain and pop on the ferry 20minutes and have a few hours in Spain.
Just a few ideas, again if you have a car or you can go by bus a nice day out is to Silves with its large Castle and Cathedral lots of Museums and some great Chicken restaurants by the river.

We've been to the Algarve a few times and have always hired a car. We were able to go all over the area (even did the trip to Spain) and visited some out of the way beaches, little villages, and another advantage was, that if we didn't like the look of a place we could soon leave. You do come home from your holiday feeling that you've 'been away' when you get out and about and explore

Thanks for those helpful replies. Faro is a definite now! Have been looking at Tavira for a possible future hol to Portugal so might leave it for then.