HITORI is a logic puzzle with simple rules. The puzzle starts with a grid full of numbers. You need to determine which numbers to remove (black out) so that a number doesn't appear twice in any row or column.
The only other rules: 1) No two black cells can be touching either horizontally or vertically. 2) The other (non-black) cells must join together to form a single large area.
All puzzles are solvable by pure logic alone with no guessing required. Give it a try.
There is another version here which you may like to try once you get the hang of it too. There are fewer advertisements and side links if you prefer to avoid those types of things.
SHIKAKU is another great Japanese puzzle in which you have to divide a space into rectangles of a given size. The link to the left takes you to a variation called Fields Separation in which you have to create fences around houses so that each property has a rectangular field of given dimension. Give it a try.
If you'd like to printed copies of this type of puzzle to take on a road trip, try this website.