
Parque Eduardo VII looking toward the Marques de Pombol statue, Avenida Liberdade, the Baixa, and the Tejo River
If coming from the US, you probably took a Red Eye. Hopefully you got some sleep, or something sleep-like, on the flight.
Now let the fun begin!
But first, a bit of advice...
The Lisbon airport is notorious for widely variable experience on arrival due to immigration and custom. But one thing is consistent: there isn't really a bathroom between the jetway and the terminal, so at least a half hour before landing squeeze out a whiz. It is possible you'll cruise through immigration in five minutes, and possible you'll wait for hours and hours to get through.
On exiting the airport, go left for a cab, more or less straight to the parking lot for arriving Bolt or Uber rides, and right for the Metro.
The Metro is the most fun. You'll want the Via Viagem card anyway for more metro-ing, busing, and ferrying during your trip, so might as well get it now.
Take the escalator down into the Metro where you'll find a line up of ticket machines. Touch the screen, hit the British flag icon for English, and buy a rechargable card. If you put €20 on it you should be fine for quite a while.
As at all ticket machines everywhere, be leery of people trying to "help" you unless they're wearing the vest and badge of official Metro workers.
There's only one line at the airport, the Vermehlo (red) line, and the airport is the end of the line, so don't worry about getting on the wrong train. Review the maps on the wall relative to wherever your hotel is and get off at that stop. The Lisbon Metro requires scanning your ticket both on ingress and egress.
Most people in Lisbon for the first time want to go right to Alfama for the "authentic" Lisboa experience. We'd recommend waiting for tomorrow.
If you took the red eye, you'll be tired both physically and mentally. Alfama is a lot to take in.
It is super hilly, and you could ride a tuk-tuk to the top, but a) we hate tuk-tuks and b) the fun of Alfama is wandering, looking, walking. Because Alfama is so famous, and so close to where the cruise ships (sometimes as many as four a day) disgorge, it is always packed, all the time, in every season. Perhaps giving the old brain and leg muscles a break right after the flight would be appreciated.
Rather, consider easing into Lisbon, and the Lisboetta vibe, with a nice downhill amble that start super chill with a great overview view, then gradually becomes more busy and more touristy, helping you acclimate, and ends with a easy going walk along the river.

(1) Take a Bolt to the top of the park: set your destination as "Miradouro do Parque Eduardo VII". Wikipedia: Edward VII Park
Admire (or not) what looks like a pile of rocks in a dry wading pool but is in fact a sculpture celebrating the April 25, 1974 Carnation Revolution that overthrew Portugal's fascist dictatorship (yes, they suffered a fascist dictatorship until 1974!).
Start walking down the left side of the park. Those stones that make up the sidewalk are called calçadas and you'll encounter them everywhere. Be careful! They're uneven, sometimes missing, and slippery when wet.
(2) After you pass the restaurant Praia no Parque look for a mansion-like building on the left, the Pavilhao Carlos Lopes, which has very cool and very large tile art on the walls facing the park. Those blue and white tiles are called "azulejos". They are quintessential Portuguese. Keep walking southeast, downhill, until the end of the park.
(3) At the bottom of the park is a parking lot full of Hop On, Hop Off buses. If you just bushed and don't really want to walk, this might be a good time to get an overview of the whole city from the top of a double decker bus.
On the other hand, if even a little energetic, walk around the statue of the Marques de Pombal and continue down Avenida Liberdade, Lisbon's premier luxury shopping boulevard.
Sooner or later you'll see a "quiosque", which is a funny little building with outdoor tables and chairs that sells sandwiches, pastries, coffee, wine, beer, and mixed drinks. Time to take a load off, you've earned it.
Note: it is super bad form in Portugal to walk around with coffee. Coffee is meant for enjoying, with conversation and friends. So don't multi-task. Sit and sip.
Keep going southeast. The divided boulevard will eventually neck down to a regular street. Follow it as it curves gently to the left
(4) On your right look for the dual arches of the Rossio train station, carved in stone to look like intertwined giant ropes.
Continue on the southeast facing diagonal road, until you get to the D. Maria II National Theatre on your left and the Rossio Plaza, with its undulating calcadas, on your right. Walk toward the fountain then continue to the south side of the plaza.
Choose any of the southward streets - they're all different and all the same - you're now in The Baixa, Tourist Central. Try to resist the urge to buy a plastic blob thing that splats onto the table, only to reform itself miraculously.
Also resist the urge to eat at any of these restaurants. You probably already know this, but if somebody is waving a menu and beckoning you to sit, keep moving!
(5) Eventually you'll get to Praça do Comércio.
(6) At the river, pause to enjoy the people milling about, sitting on the sea wall, maybe listening to a busker play the saxophone. Then proceed to the right, westward.
Almost immediately, on a tiny bit of beach, someone has balance-stacked, then painted, rocks to form something that is either the epitome of "folk art" or a cheesy play for tourist coins. Or both.
(7) Five minutes later there is a quiosque called "Chill Spot" which is perfect for a coffee or a cold one, people watching, and maybe a DJ spinning euro-disco bomp bomp bomp music. Linger. You're not "missing anything" by sitting here, you're actually experiencing Lisboa.
(8) Keep going, past the Ferry Terminal, and you'll walk into the area called "Docas", or the docks, full of bars, restaurants, and clubs. But don't think of trying one of the clubs before about 11 pm or midnight, as you'll be the only one there. Sure would like to be able to recommend which club is the most bumpin', but alas, have never been to any of them.
(9) That's enough for one outing. Head north, inland, to find the Santos Metro station. Use your transit card to get back to your hotel for a nap, and to plan your next steps!
In total this walk is only about 4 miles, mostly downhill at first then dead flat, and is a delightful way to get a first peek at Lisbon!