Upon arrival:

At the airport you can catch the Aero Bus (between 7 am and 11 pm): you should stop at CAMPO PEQUENO.

The Aerobus ticket will also give you a 25% discount on other Yellow Bus touristic tours (Tagus Tour, Olisipo Tour, Hills Tramcar Tour, Pena Palace Tour, Sintra Tour, Fátima Tour) if these other tour tickets are bought inside the bus or at the main Yellow Bus Station at Praça do Comércio. Please visit:

http://www.yellowbustours.com/en/cities/lisbon/tours/

UNDERGROUND (Metro) from the airport (only 1 change at Saldanha): CAMPO PEQUENO is the closest Metro (Underground) station to the Hotel Zurique (four minute walk).  One Metro Ticket costs 1.50 euro, you may consider buying a one day ticket if you arrive early and want to travel more on that day.

The TAXI fare from the airport to the Hotel Zurich should not cost more than 15 euros. Sometimes, it is quicker to go to departures (right next to arrivals) to get a taxi. If you want to avoid (possible) long queues: just turn right as you come out into the main arrivals hall, keep going, go up the escalator, turn slightly left and go outside, you are outside departures, and there is no queue to get a taxi.

HOTEL AREA: Plenty of local cafes, restaurants, and supermarkets. There is a shopping centre (several restaurants) under the red bullfighting ring/concert hall open until (at least) 10 pm. Close to the underground station (there is an exit/tunnel to the shopping centre) and to the bus stop. In Saldanha (1 underground station away or a 15 minute walk) there are three shopping centres, open until 11 pm.

Once in the city, if you are using the public bus to travel around Lisbon, buy a pass (Zapping) and top it up at any underground (METRO) station, as tickets purchased inside the bus are more expensive.