Hi Esmeralda,
The best places in my opinion in Lisbon are:
Alfama, Graça, Miradouro da Nossa Sra. do Monte (lookout), Terreiro do Paço (also named Praça do Comércio) is great! Also Miradouro da Graça (lookout), Chiado - Brasileira, Lg Camões, Carmo ruins, Sta. Justa Lift, Miradouro do Admastor (lookout), Tram 28 or 18 (but watch the pickpockets - this is the most common robbery in Lisbon, a police offcier told me a dew weeks ago!). Also Rossio and Praça da Figueira are a must see! Belém very good also - Torre de Belém, Jerónimos Monastery, Padrão dos Descobrimentos, Centro Cultural de Belém! Also try to visit Sintra - which is beatiful - get there by train - watch out on that train line - petty crimes can occasionally occur, no more than that.
Also try to visit Guincho, Cascai - you can get there by train from Cais do Sodré. It is a very nice train ride, because you always go by the sea... ;)
In the evening the most active and diverse place is Bairro Alto, which is very near Chiado. This is a small district with a strong night life, with many pubs with many diferent types of music - reggae, pop, rock, 80s, drum n bass, etc etc...
But the nicest thing of Bairro Alto is the people that desnsily populate the streets (more on friday and sat night) and just chat, talk, meet each other.. is a very social and very diverse place.. you have bars for indie people, reggae fans, electronic music fans, gay people, evrything! That's the beauty of this district!
If you are into the 80s music, can also check a nice bar which is Incógnito, that is near Bairtro Alto (in the Calçada do Combro) about 5min walking from Bairro Alto)
Portugal and specifically Lisbon is a calm city. No violent crime happens here. Can occur pickpocketing or not violent stealling, if you "make it easy". During the day, no one will harass you no problem (well..just watch out for the Hash salesmen street team in Rua Augusta - downtown - which is also must see!!)... this during the day. During the day avoid being alone in dark places, and if you see strange people with strange atitude, try to move with a low profile.. But the most most most likely is that nothng happens! If you go to Bairro alto, be there in friday or Sat evening, because that's when you have more ppl there.
Ah, and you also shell check a Fado House. There's a very good one on Bairro Alto, which is called "Já Disse".. well.. I'm saying it's good because you don't have to pay dinner, etc etc.. and can be cheap... If you want something more expensive but also with more quality, can go to Parreirinha da Alfama, Luso,... search in Bairro Alto.. there are many!
Ok, I think that's enough... hope it helps!
BTW, are from Switzerland?
If yes, how come do you have that latin (portuguese?) name!? Daughter of emigrants?
Hope you enjoy Lisbon to the fullest!
Lisbon is a very very beatiful city... my favourite, I must say! ;)
Joao