I would definitely NOT recommend walking up to the Olissippo Castelo hotel on arrival! The climb is very steep and unless you know exactly where you are going through the old alleys and stairs you can waste a lot of time. You will find it a real problem with a suitcase.
I know this, as it it is near the Chapito theatre and restaurant, which I frequent sometimes when in Lisbon.
So, I recommend that you do one of two things, bearing in mind taxis are not expensive in Lisbon:
1) Take a taxi direct from the airport to the hotel. probably less than € 15.00 depending on time of day/night & no. bags.
2) Take the Aerobus 91 to Rossio as Cubsur says, cross over the square to Mcdonalds, turn right and you will see the Teatro Dona Maria II. In front of you and to the right of the Teatro Dona Maria II you will see a taxi rank. Grab a cab.
Probably less than € 6.00 time of day/night & no. bags.
Bear in mind that it will seem a long journey up to the hotel, and you may think that the driver is up to one! However, with the one way street and control access system in the Alfama, Se and Castelo area, taxis have to go all round the house to get there.
However, take my word for it you do NOT want to walk up there with suitcases!!!
The Hotel has a great view over Lisbon. For a view of the river, if it's a nice day, walk down to the Restaurant Chapito at Costa do Castelo, nº 1 / 7, 1149-079 Lisboa - Portugal
Best at lunchtime with a wonderful view from its terrace over the Tejo to the South.
