Carcassonne is the standard answer for someone who insists they do not like board games. It is also the cheapest pick here, which makes it an easy first purchase, and it comes with real pedigree: a 2001 Spiel des Jahres winner that has stayed a genre cornerstone for over two decades.
The loop is simple. Draw a tile, place it to extend cities, roads, and fields, then drop a meeple to claim whatever you build, and that simplicity hides a surprising amount of strategy once you start contesting territory with other players. Because the tiles come out randomly, the map is different every session, so it never plays out the same way twice.
It works for kids age 7 and up but still gives adults plenty to scheme over, which is a rare combination. The tradeoffs are minor: it has a calmer pace than a party game, and farm scoring is the one rule that reliably confuses a first-time player. It is the best two-player game of the three, and BoardGameGeek's community poll names two as its best count.