To view all the major attractions in two days, you'll have to get up early. Start at the Rossío, the main downtown square, and stroll through the Baixa, pausing to window-shop or take a coffee. Wander into the Alfama quarter by way of the Sé, following the winding streets past lookout points and churches as far as the hilltop Castelo de São Jorge. The views here are magnificent, and you can grab lunch at one of the many nearby cafés and restaurants. A tram ride takes you back down to the Baixa, where, in the riverside Praça do Comércio, you pick up another tram for the rattling ride west to Belém and the magnificent Mosteiro dos Jerónimos, the acclaimed Torre de Belém, and the Padrão dos Descobrimentos. On the way back to the city center, stop off at the Museu de Arte Antiga.
Your second day can be less hectic. Head up to the Bairro Alto and the Chiado shopping area and spend the morning browsing in galleries and stores, visiting the Igreja de São Roque and popping into the Instituto do Vinho do Porto for a glass of port. Have lunch in one of the small taverns or restaurants, and then return to the Baixa via the Elevador da Glória. Take the metro uptown to the Fundação Calouste Gulbenkian, where you can spend a few hours viewing the collections in the Museu Calouste Gulbenkian and the adjacent Centro de Arte Moderna. Alternatively, take the metro to Parque das Nações to visit the Oceanário de Lisboa.
Spend the first morning in the Baixa, where the shops and cafés are inviting. At the riverside Praça do Comércio, take a ferry across the river and back for fine city views. Have lunch in the suburb of Cacilhas, where the ferry docks, or return to Praça dos Restauradores, just north of the Rossío, where a side street just off the square—Rua das Portas de Santo Antão—is lined with well-known fish restaurants. Spend the afternoon in the Alfama, taking in the Sé, the Castelo de São Jorge, and the Museu-Escola de Artes Decorativas.
On your second day, catch a tram out to Belém. Spend half the day exploring the monastery and monuments; you'll also have time for at least one of the specialty museums—Museu da Marinha, or Museu Nacional de Coches. On your way to or from Belém, stop at the Museu de Arte Antiga.
Split your two remaining days between old and modern Lisbon. One full day should involve seeing the Chiado shopping area and exploring the Bairro Alto. Be sure to pop into the Convento do Carmo's archaeological museum and make a side trip to the Jardim da Estrêla, or you can spend more time at the Oceanário de Lisboa.
On the final day, walk the length of the boulevard-like Avenida da Liberdade to the city's main park, Parque Eduardo VII, where the greenhouses are a treat. From here, it's a simple metro ride to the Museu Calouste Gulbenkian and the Centro de Arte Moderna.