The trick to Montevideo is that its best experiences are not really attractions at all — they are things you do rather than things you see. The city has museums and monuments enough, but what stays with people is the smell of woodsmoke at the port market, the Sunday crowds on the Rambla, and the slow ceremony of an afternoon that nobody is rushing to end. Plan lightly and leave room to join in.
Eat at the Mercado del Puerto. Under the wrought-iron roof of the old port market, a row of parrillas fire up wood grills every lunchtime, and the ritual — a glass of medio y medio, a plate of grilled meat, the buzz of a room full of locals and travellers — is the essential Montevideo meal. Go hungry, go at lunch when it's liveliest, and don't over-order; the beef here does not need help.
Walk Ciudad Vieja and the Rambla. Spend a morning among the old town's grand, weathered facades — the Plaza Matriz, the Teatro Solís, the pedestrian streets down to the port — and an evening on the Rambla as the sky goes pink over the river. Time it for sunset near Pocitos and you'll understand why Montevideans treat the waterfront as the city's shared front garden.
Feel the football, even if you don't follow it. Uruguay's devotion to the game is genuine and infectious, and the Estadio Centenario, home of the very first World Cup final in 1930, has a small museum worth an hour even on a non-match day. If there is a game on and you can get a ticket, the atmosphere is something few travellers forget.
Then simply slow down. Linger over a cortado in a Pocitos café, share mate with whoever you're travelling with on a bench by the water, browse the Sunday antiques and bric-a-brac at the Tristán Narvaja market. The best day in Montevideo is rarely the busiest one — it's the one where you let the city's own gentle pace carry you along.