The catalog compiled by Koechel lists 626 works. Famous might arguably include the Requiem and several operas including Don Giovanni, The Marriage of Figaro and The Magic Flute. the overture to the marriage of figaro
There was no one particular "place" that Mozart would compose. He always had paper with him and made sure there was ink and a quill nearby whenever he had the urge to write music.
The piece that would be recognised by almost everyone, even if they couldn't name the composer, would be the opening movement of "Eine Kleine Nachtmusik", (Serenade in G, K525). Very well known also...
"Neither a lofty degree of intelligence nor imagination nor both together go to the making of genius. Love, love, love that is the true making of genius."