If you want to experience a part of Lisbon that's not all about shopping opportunities, but about feeling the real Lisbon, where people live and where you'll find portugese people in the cafés, this is the place to visit. There's also a lot of beautiful scenic views especially along Largo Santa Luzia & Rua Säo Tomé. Note you can take tram 12 from Praca da Figueira in a circle trip or get of and walk part of the way (and get on Again if you like). It's easy to get there (Praca da Figueira) with the Metro.
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