Lagos is more for relaxing on a beach in season will be crowded with other beach goers ; but definitely some cliff side trails all around where you could escape the crowds. Further west of Lagos on or near the Atlantic side does not get as visited but could be lacking in conveniences.
With 8 days, you could definitely do 4 nights there with a car and then 4 nights in Lisbon without a car.
I am staying this year in a small town on the water just west of Sintra so close to Lisbon but a little more off the main tourist path, could be an option for you. Look up Azenhas Do Mar ; will still be quite crowded with tourists in the summer since it is also on the water/beach but less so than the Algarve and much closer to Lisbon. In Sept I think would be not crowded. You would want a car for this small area though.
Lagos probably best option for kayaking, Atlantic side is likely too rough for that.