Now, I know what you're thinking, you can get jigsaw puzzles everywhere. Why are you mentioning them? But I don't think most people realize how diverse jigsaw puzzles have become, or how cool.
For example, Bits and Pieces in Canada (I've used this company several times), and The Puzzle House (found using a quick google search, I've never bought from them before) list quite a number of different puzzle types: 1000 piece, glow in the dark, shaped, 3D and 4D to name the more unusual.
My husband bought me a glow in the dark puzzle from Bits and Pieces (unfortunately they don't have that particular one on their site anymore). Not only was it challenging to put together - the pieces not being the traditional jigsaw shape - it looked fantastic in the dark (once you ran a strong flashlight over it to 'charge' the glow in the dark paint). Here's one they do have in stock, under normal lights and our train puzzle, glowing.
Shaped puzzles look cute, so if you can find a shape your recipient likes, that's a bonus. They're usually smaller puzzles though, so don't pick one of those if you want to give them a challenge.
If you want more story with your puzzle, I stumbled across mystery puzzles at a boutique shop on a trip up North. You can buy similar things online at places like The Puzzle House or Are You Game. The one I bought was an Alfred Hitchcock mystery jigsaw that requires you to read a small book about various characters who, in this puzzle, have 'an unusual "obsession" with Alfred Hitchcock and his films'. You then assemble the puzzle - which doesn't match the cover (so you can't cheat and see what the puzzle's supposed to look like while assembling it), and then solve the mystery.
Or you can just go with nigh impossible black and white 1000 piece puzzles, like High Security by artist Thomas Barbey (available, among other places, at Boardgames.ca) which my husband recently finished. I helped with the castle. :)