The free or nearly-free activity inventory across the cities I've traveled most is worth sharing because guidebooks undercount these.

Bangkok: the Grand Palace area temples (Wat Pho is $5, Wat Arun $1, many other temples free), Chatuchak Weekend Market (free, extraordinary), the various canal boat trips using the public express boat service ($0.50), BTS Skytrain station viewpoints, Lumphini Park.

Hanoi: Hoan Kiem Lake and Turtle Tower, the Old Quarter walking circuit, Ho Chi Minh Mausoleum (free to queue and view), Women's Museum $1, the train street (free, though the cafés along it charge for drinks), Temple of Literature $1.50.

Lisbon: Parque das Nações waterfront walk, Belém riverside free (tower is €6 but viewable for free from outside), LX Factory weekend market (free entry), miradouros (viewpoint terraces throughout the city, all free), Museu do Azulejo (blue tile museum) free Sunday morning.

Budapest: the riverside Pest promenade, the Buda Castle district (castle exterior free, museums within charged), Gellért Hill and Citadella for panoramic views, the ruin bar district (free to walk through, just pay for drinks), Margaret Island (free park), Heroes' Square.

Berlin: the East Side Gallery (free outdoor gallery on the Berlin Wall), Tiergarten, Tempelhof Field (former airport, now giant public park), the Jewish Memorial (free), most major museums free on specific days or evenings.