Lisbon and surrounding in nine days
For your Lisbon time, it truly makes sense to stay in Lisbon. The city has reasonably good public transit, and you won't need (or be able to do much with) a car. If you stay out of the city, you'll be spending time heading in and out every day.
Rail access to Sintra and other nearby places for a day trip is good.
I would avoid a day trip to Porto; by the time you've made your way there and back, there won't be much time left between. If you really want to do Porto (and I do love it) you really need to plan on an overnight, but that may be more time than you want to invest.
I'm not a beach person, so i can't offer much advice there; perhaps others will.
Do expect to spend a lot of time walking up and down hills. Do expect to find a lot of really good food at really cheap (if you're not on Portuguese wages) prices. Our watchword for Lisbon is "Cheap but steep!"
And despite what some people may tell you, Lisbon has plenty to take up your days; some people told us that it was a '3-day city' and boy, were they wrong!