Absolutely love Lisbon, been three times in the last couple of years, it just feels such a happy place.
Don't bother with a taxi from the airport if you are staying centrally in Lisbon, either take the Metro which is an easy trip with just one change, or the Aerobus (slightly more expensive) if you have lots of luggage.
Public transport in Lisbon is truly excellent - hop on and off buses and trams etc all day long. Use Citymapper, fantastic app and covers Lisbon.
Buy a Viva Viagem card for transport - in fact we always had two types, a 24 hour pass and a zapping pass as they offer slightly different options - information here Lisbon Guru - much better value than single tickets.
Take the ferry from Cais de Sodre to Cacilhas (10 min trip) and from there you can take a normal bus to the Cristo Rei monument - and go up in it if you don't mind heights for fabulous views over the river and Lisbon on the other side.
Also from Cacilhas there is a walk (turn right out of ferry port) along the river side (a bit seedy at times but busy and interesting) - there's a little restaurant about 20 mins walk away Ponto Final - fresh fish, excellent value sitting right on the riverside (it will splash you if you sit too close!) - one of the highlights of our last visits, this, and the back streets here are interesting to explore on foot if you go up the steep elevador just past the restaurant.
You will (as history/culture enthusiasts) definitely want to take the tram (15) to Belem - go to the Pastelaria de Belem for the famous custard tarts and coffee (don't queue at the door for takeaway, walk right in to the tables area - coffees and a plate of tarts cost under 10 euros, well depends on how moreish you find the tarts 
- then walk to the Monasteiro (free entry on Sundays but we just admired it from outside) and the lovely little Torre de Belem, and the wonderful monument des Descobrimentos.
You may be fluent in Portuguese but if not, thank you is Obrigada (if female) and Obrigado (pron Obrigadoo) if male.
Lisbon is so small for a major city and highly walkable, but it IS very hilly, so use those trams and buses as much as poss (unless you're young and fit, unlike me 
Have a fabulous time 