@randomhornIt's subjective but if you can I think you should take it from the BigD, so to speak. If you only have a week I'd stay in Lisbon and the smaller cities or towns that are close by. A lot of the charm of Portugal is found in the smaller cities or towns. Consider also Aveiro and Costa Nova.
You might think about hiring a driver to take you straight from LIS to Lagos. We just did that - hired a guy with a Mercedes Sprinter. Saves an entire travel day. (We used a travel agent but I got the guy's card - feel free to dm me if you want the contact.
Lagos is definitely touristy btw so be prepared.
Should add - I'm in Portugal now. Duoro Valley. We've been in PT for 10 days and weather has been phenomenal. Started out in the Algarves, then drove a couple hours to the Alentejo region, which reminds me of a prettier version of the Hill Country, then to the DV. It's been a great trip and still have 10 days.