São Jorge is the easiest one where you have the castle, the oldest part of the city. For drinks around you have Chapitô, a bit expensive but good. The castle is worth a visit, especially for the view, take the tram 28 from Baixa (map of buses and trams) and enjoy the typical transport of Lisbon.
Using the same tram you should also pass by Sé de Lisboa, the main cathedral that accommodates the typical marriages of the 12th of June because Santo António, the patron saint of Lisbon, is also the patron saint of marriages. Behind you, there is Portas do Sol which have a nice view over Alfama and the sea. Go to the bar for a drink but to have food go down to Alfama and pick any restaurant, food quality is generally good there. Try Parreirinha de Alfama if you go there at night, they should have some Fado, sad but beautiful music!