On day 2, we headed out to Belém - a historic district on the southwest outskirts of Lisbon. Belém sits on the mouth of the Tagus, so you get some gorgeous views of the river. There are multiple public transportation options for getting out to Belém. We had originally planned on taking a taxi to the main subway station in Lisbon then a train out to Belém from there. However, our taxi driver informed us that it would only cost €15 to cab straight out there. For a few extra euros, we would essentially be saving 20 minutes of travel time. It was a no brainer. FYI - taxis in Lisbon are really inexpensive and quick. They are often a more sensible option (particularly if you are traveling in groups) than public transportation, which isn't as extensive or frequent in Lisbon.
The main sites to see are the Belém Tower, the Jerónimos Monastery and the Berardo Museum. The tower and monastery are perfect examples of Manueline architecture and 15th-16th century Portuguese supremacy. Make sure to go early to beat the crowds as the queues can get fairly long.
A short walk from both sites is the Museu Colecção Berardo. Seldom packed, this museum features a great collection of contemporary and modern art from around the world. Even better, admission is free.
When in Belém, don't miss out on Pastéis de Belém. This massively popular cafe/bakery is listed on every travel guide, and for good reason. The pastel de natas (egg custard tarts) were the best we had in Lisbon.
About a 10 minute walk from all the major sites in Belem is the Fundação Champalimaud. This biomedical research center (yes, you read that right) happens to be one of the most striking buildings in Lisbon and a great place to explore.
With a few hours of sunlight left, we decided to head back into the center of the city. Tired of walking, we opted to take a trip on the historic tram 28 route. The city is lined with mini trams that rattle up and down the endless hills and take you through the various neighborhoods. Finally, before calling it a night, we squeezed in some shopping at Entre Tanto indoor market, a glass (or 2) of wine at Poison d'Amour and dinner at O'Prego da Peixaria. All 3 places are in the beautiful, swanky neighborhood of Principe Real.
Make sure to check out my "3 Days in Lisbon" map if you want to learn more about each location, and look out for Day 3 tomorrow!