You may realise that Baixa (downtown) is like a valley. If you have the river in front of you, Castelo, Graça, Alfama and Mouraria are to the left of you but you also have more hills on the right side. Starting by Chagas where you have Convento do Carmo you should go there by taking the old lift in Rua da Prata. Yes, prata means silver, in Baixa many streets have the name of the goods they used to trade there, gold, silver, etc. Actually, by the river you have Praça do Comércio which means Commerce/Business Square. If you go there, go to the top of Arco da Rua Augusta. Going back to the old lift, the name is Elevador de Santa Justa, you do not pay much and the view is totally worth it. Alternatively if there is too many people in the queue just take the first right (that goes up) in Rua Garrett (name of a theatre writer). Actually before going up get an ice cream in Santini. Originally from Cascais, they are one of the best Italian ice cream you can get in Lisbon, the other one is Nanarella, in my opinion - see below where to find it. If it is rainy forget Largo do Carmo and go instead to the bar on top of Hotel Chiado close to Santini. If not, in Largo do Carmo you have the new bar "Topo Chiado" which serves nice cocktails and proper gins with a great view, similar to the one of the old lift. Largo do Carmo is very important to Portugal because it was where the dictatorship gave up to democracy, on 25th April 1974. Close by you have a nice old restaurant called Cervejaria Trindade and you also have Bairro do Avillez, owned by a two Michelin star chef but not expensive.