A couple of years back I attended a conference in Lisbon and rented a bike. I hopped a train to Sintra, and then rode around along the coastline. My route was something like: Sintra, Lourel, Cabriz, Fontanelas, Almocageme, side trip off to Cabo da Roca (westernmost point in continental Europe, but NOT Europe, as I learned in Ireland this summer), then around along the ocean ultimately to Cascais. From there I took another train back into Lisbon. I want to say my route was maybe 45 - 50 km. You could easily add considerably more distance by skipping the train, but I was told that the riding closer into Lisbon was less scenic and more nerve-wracking with traffic. No doubt there's more 'high value' riding to be had in the same general area I was poking around. In the immediate vicinity of Sintra there is some highly scenic and hilly terrain to be had, but I chose to avoid them. (There were still some nice hills along portions of my route, but coming from Chicago I'm really not able to jump straight into the more serious stuff.) I really enjoyed the riding that I was able to do. There was a high concentration of motorcycle traffic, but everyone got along just fine.

Hopefully local experts can flesh this out with more detailed/varied suggestions.