The decision you are really making in Lisbon is how much hill you are prepared to walk, because the city punishes a plan that zigzags between the top of Graça and the riverfront three times a day. The version below walks each neighbourhood once, in the direction that means you climb once and coast the rest of the way, and it puts the big monuments on the days when the light is worst so that the golden hours stay free for the miradouros.
I live twenty minutes from Baixa and I run this loop for visiting friends. Three days is the point where you stop collecting viewpoints and start recognising streets, and it is enough for the historic centre, Belem and one proper excursion out of town.
Day one: Alfama and Mouraria, low to high

Start at the Sé cathedral at opening, walk down through Alfama to the river, then turn north and climb once through Mouraria to Graça. The order matters: Alfama's lanes are easier downhill with the light behind you, and the final climb to the Graça miradouro lands you at the best sunset terrace in the city with ten minutes to spare.
Eat lunch early or late, never at one o'clock, because that is when the tour groups take the tables near the castle. Two options a street apart from each other: a counter with grilled sardines in season (June to October) or a tasca serving caldo verde and a plate of clams for under 15 euros. The Castelo de São Jorge is worth the 15 euro entry for the view rather than the walls, and it is quietest in the last hour before closing.
Day two: Belem, the river and the pastel route
Take the tram or the train from Cais do Sodré to Belem in the morning and do the monuments in a line: Jerónimos monastery, the Discoveries monument, the Tower of Belem, then the Coach Museum if it rains. The monastery cloister is the one to pay for; the queue at the tower is rarely worth the forty minutes it costs.
Lunch in Belem is a trap for anyone who stops at the first pastelaria. Walk two blocks inland and sit down for a proper meal, then go back for the pastel de nata where it is made: the original bakery still sells them warm and you eat standing at the counter for about 1.50 euros each. Take the riverfront path back towards Ponte de Lima and spend the late afternoon in the gardens rather than on the tram.
Day three: choose between Sintra and the city
Sintra is the obvious day trip and it deserves the choice: forty minutes by train from Rossio, then the bus up to the palaces. Go on a weekday, buy the Pena Palace time slot before you travel, and start with the Moorish castle rather than Pena, because everyone else starts the other way round. Come back for a late dinner in Bairro Alto.
If you would rather not leave the city, swap Sintra for a slow loop through Príncipe Real and Campo de Ourique: the market hall for lunch, the botanical garden for an hour, and the flea market on Sundays at Campo de Ourique, which is where Lisbon actually shops. End with petiscos and vinho verde in a small place with no sign, which is the pattern of most good evenings here.
Getting around without losing an hour
The metro is flat-fare and clean, and it beats the trams for distance. The historic trams 28 and 12 are a moving queue: ride them at the first stop, before eight in the morning or after seven at night, and you will get a seat; at midday you will be standing in a corridor of backpacks.
Buy a reusable card at any metro machine and load it with zapping credit rather than paper tickets, because the same card covers the metro, buses, trams and the train to Sintra at a discount. Taxis are metered and cheap by western European standards, and Bolt is widely used; from the airport to the centre is around 15 euros at any hour.
Where to eat, by hour rather than by rating
Breakfast is a bica and a pastry, standing, for under 2 euros. Lunch is the big meal: the prato do dia chalked outside will run 8 to 12 euros and include dessert and coffee. Dinner starts after eight and the fish is what you order, because Portugal's fish arrives in the morning and the kitchen knows it.
Two reservations are worth making ahead: a table for grilled fish in Cais do Sodré on a Friday, and anything in Alfama on a summer Saturday. Everywhere else, arrive by seven-thirty or after nine-fifteen and you will eat well without planning it.
The one thing to sort out first
Book your Sintra palace slot or your Friday dinner, and then decide where you sleep: Alfama if you want atmosphere and stairs, Baixa if you want flat ground and transport, Principe Real if you want quiet. Everything else in these three days can be improvised on the morning you feel like it.
What to book and what to leave
Reserve the Sintra palace slot and the Friday dinner, then keep everything else loose. Lisbon rewards a plan with gaps in it: the miradouro you find on the walk back, the market hall you step into because it starts raining, the fado house that has one table free at ten. Three days is enough for the historic centre, Belem and one excursion, and it is not enough for a second city, so resist the suggestion to add Evora on a day when you have not yet seen the Alfama lanes by daylight.