If you want to answer this in 1 conditional statement, regardless of which direction the NPC is from the player avatar, try this:
player.distance_to(npc) <= 1
(where player and npc are Vector2s of the tile position on the tilemap, though you could do something similar with co-ordinates if needed).
Basically this measures the euclidean distance between the two, and in tile-space that distance would be equal to 1 if you're either of the spaces horizontally or vertically adjacent to the NPC.
If you wanted to include diagonals, that would be equal to sqrt(2), so 1.41, so if you did:
new_position_on_map.distance_to(destination) < 1.5
you'd get what you wanted.