Trapped for life on a remote island; then you might want more substantial amusements.
But for a half dozen to leave out on a coffee table, consider these ...

Traffic Jam

Great graphics with precisely sized heavy plastic pieces that are fun to use. When you are tired, just slide on the box lid (no bag of unassembled stuff to worry about). The pieces can also be used for a host of other puzzles (Red Donkey, Century, Ushi, etc.). Easy to 3D print the pieces and also the tray, or craft the tray from wood; finish by making a cardboard sleeve,

Easier than Rubik's Cube but still quite a challenge. Other fun choices are Rubik 2x2x2 (a bit harder), Rubik 2x2x3 or Rhombi Diamond (easier), Dino Cube (even easier), Six Spots or Pyraminx Duo (much easier). Versions of this puzzle are commonly available for purchase.
Giga Burr

A triumph of computer assisted design by one of the great puzzle designers. Quite hard for just three pieces. Yes, when you are tired you are stuck with loose pieces, but there are only three! Try also the Cubie Burr. Can be home made by one handy at wood working, or also a nice 3D print project.

Has a booklet with many fun shapes to make. Made for hundreds of years, new versions are commonly available, and it is easy to make one yourself. The Richter Co. that made the version shown here, also made many other fun puzzles of a similar type (Cross Puzzle, Sphinx, etc.) The pieces are a very easy 3D print project, and can be stored in a small box or bag.
Ball And Ring

The simple but impossible look makes it fun. It is straightforward once you see how; however, after putting it away for a few months, it can be like starting all over. Easy to make; use a fun object for the block and make the loop an unusual shape. Try also the Moving Rings or WitsEnd.
Hinged Cubes

One of the first puzzles people tend to pick when they are confronted with a bunch of puzzles. Not too difficult, and there is something very nice about the feel of the hinges. So if some of these other puzzles are too difficult, try this one. Not too hard to make one; or if hinges are too much work, use some small wood blocks from a toy store joined by tape.