My only trip out of the capital was to the town of Sintra, which is accessible by a cheap and easy 40 minute train ride from the restored Rossio Station.(Broadway Malyan Architects).
Sintra is a UNESCO World Heritage site, set in steep hills, with many fine old buildings, villas and gardens to see. It is topped by the Castelo Dos Mouros, the Moorish castle. There are buses serving some of the route. I chose to walk most of it, which given the midday sun may not have been the smartest thing to do and when you want a shop selling bottled water they just don’t appear – nor even a bar with a cold beer. However, the effort was well worth it, the remains of the castle fascinating, and the views from the top quite spectacular.