Hello toastedmallow, Obidos is a great place to visit one we looked foward to visiting when we were there, not sure about local transport it about a hour from Lisbon. When we went we did it as part of a day tour booked through our hotel in Estoril and I must say it was one of the best tours we have ever been on, it went like this.
Pick up at our hotel and then on to Edward 7th park in Lisbon to get the main bus, from here we went to Obidos for a hour and then on to Alcobaca to see the largest church in Portugal with the tombs of King Pedro and Ines de Castro (a great love story) from here we went to the seaside town of Nazare for lunch and walk round. After that we went to Batalha built to celebrate the victory over the Spanish 1385 again with tombs of some kings of Portugal, Joao 1 and Philippa of Lanchaster and there sons one of hume is Henry the Navigator. Last on the tour was Fatima for a bit of holyness.
You can also see this tour on the below website under tours from Lisbon.
http://www.portugalvirtual.pt
Dave