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Just a few notes. 

Our visit was too short to allow us to pretend to be experts on this world-class cities.  What follows are miscellaneous impressions.
Above all, our advice is "Go to Lisbon, and go soon."  I say this because the city is undergoing a transformation and its peeling walls are being replaced by renovation that is turning its buildings into jewels.  There is nothing wrong with that, of course, and today's Madrid is testimony to the polish that labor and money can give to an old city.  The problem is that the whole ethos of Lisbon has been one of longing for past glories; the romance of Lisbon has been neighborhoods in delicious disarray.  The Lisbon that emerges from new-found properity and investment from the European Union will be a beautiful city, but it will not be the city that has attracted writers and authors for centuries.  Visit this city now, and then return again later!
Take note of the main neighborhoods from your guidebook.  These have very different qualities -- Alfama, Baixa, Chiado, Bairro Alto and Estrela, Belm.  During a short visit, you may not have time to visit them all, but you can see a lot about the contrasts between the neighborhoods from your taxis.
Take a taxi or a funicular rail to Castelo de So Jorge and get your orientation.  This is a wonderful place to view the whole city, including places you may not have a chance to visit, such as the ruined convent church of Igreja do Carmo.
Coffee at Caf Brasileira is a great way to begin a walk around Chiado and the Bairro Alto (corner Rua Garrett and Rua Nova da Trindade).  You will find antiquarian bookstores and many other interesting shops.  Make your way toward the Church of St. Rock (A Igreja de So Roque) where its chapel of St. John the Baptist is a masterpiece.  This chapel was fabulously expensive when King John V built it from 1742 through 1750.  It includes rich marbles and precious and semi-precious stones.  Some of the panels and the floor are mosaics, but with pieces so fine and so tiny, that it is hard to believe that the glittering appearance is not seamless.
Lunch in the near-by Trinidad Beerhouse offers the setting of a former monastic canteen, with splendid tiles.  (Rua Nova da Trinidade, 20 C.)
The Monasterio dos Jernimos is a kind of Westminster Abbey for Portugal, with tombs of poets and royalty.  The scale of this monastery is immense.  The convent is particularly beautiful.
Don't miss the Museu Nacional do Azulejo (the National Museum of Tiles), even though it is a taxi-ride.  If you can visit only one museum in Lisbon, this would be it.  Portuguese Tiles - Azulejos
The Baixa neighborhood includes the main shopping district.  The Elevador de Santa Justa, built by a student of Gustave Eiffel, offers a view of the neighborhood.  Rua Augusta is pedestrians-only shopping street.  Cervejaria Portugal (Rua Augusta 238-240) is a fine seafood restaurant.  Ask to be seated upstairs, which is quiet and offers views of the district.