Hi Karen,
Having just returned from 2 weeks in Portugal, with time split between the Lisbon area and Lagos in Algarve, I may be able to offer some suggestions for these locations.
First of all, Lisbon itself, takes 2-3 days alone. Put on your walking shoes and head out and explore. I based in Chaido, right on the square, and then headed out in basically 2 directions. The three neighborhood walking tours in RS Portugal book was an excellent reference. I found that going high was a good way to start, working past the elevator and large square (name escapes me), and then heading up towards the castle. (PLEASE NOTE: pickpockets abound. I am now the owner of a new iPhone thanks to a clever individual who liberated the old one from my pocket.). From the top of the hill, it was wonderful to just head back down through one of the main neighborhoods. I went down through Alfama on the last day, and that is not to be missed, particularly if you take the small staircases, and end up is some very interesting places. Much fun! and at the bottom, a river walk is always delightful, ending up in the other big square right on the river.
While it does not seem to be covered much in the guide books, I found Cascais to be wonderful. I spent a week based there, really to much if you are in country to sight see. But I was there to check out potential living locations. Cascais is much more relaxed than is Lisbon, and really does not have a lot to see, but it makes for a nice day trip to take the train towards Lisbon a few stops, have a look at the neighborhoods, and then walk back to Cascais along the water. Mine was a relaxing trip, not one of seeing everything, so yours will be different I'm sure.
I took a bus from Lisbon to Algarve, although I was told that the train was also very nice as well. And I spent my time in Lagos while there. It is very different from the Lisbon area in that it was almost exclusively reliant on tourism. The food was good, and the sights OK, however I would not recommend spending a lot of time there. In my case, I may have stayed a day longer than was needed, but we did get a nice day of bike riding to the next town (Luz).
Other things that were seen around Lisbon/Cascais included renting a car and heading up the west coast for a bit. There was a stop in Sintra, along with a big rain storm. Not sure I could recommend driving to Sintra, in that the bus service there is very good, and parking is very hard. I also continued north up the coast to a town called Ericiera. This was an accident, but it turned out to be a wonderful accident. Very beautiful little town that appears to cater to surfers. An old guy in the park told me it used to be fishing, but no more. If you are planning to head up to Porto by car, worth the stop, if only for lunch.
Jim