One of the best travel companions is your imagination.

Picture yourself in the oversize whirlpool bath of a luxury tropical villa on stilts with a seaside view at the Pangkor Laut Resort, nestled on a private island off the west coast of Malaysia. Condé Nast Traveller (United Kingdom edition) rated this Xanadu the number one resort in the world in 2003.

It would be great to have a rooftop apartment in Paris or a historic chateau in the French countryside at which to vacation, n’est pas? If you agree, but can’t afford such luxury, try this substitute: paris-fineresidences.com. This real estate brokerage website offers “a rare and vast” collection of sophisticated Parisian town homes fit for princes of commerce, as well as castles for would-be royalty.

There’s more than a grain of truth in the maxim, “It all depends on how you look at it.”

Dutch artist Marrits Cornelius Escher (1898-1972) proves the point with his etchings of impossible structures at the mind-boggling website mcescher.com. In addition to fantasy buildings with tricky perspectives, there are six galleries of symmetry drawings, including Escher’s famous repeating patterns of geometric shapes, such as flying fish in a herringbone formation.

Feel as if you’ve seen it all? Renew your vision at earthscienceworld.org, with an image bank of more than 7,000 often breathtaking photographs of desert dunes, lightning storms, waterfalls, volcanoes and myriad other natural phenomena from around our world. (And off of it, in the case of images from some of Earth’s sister planets.)

Light up your neurons!

Discover your “riddle-solving quotient” at justriddlesandmore.com, where you can ponder dozens of brainteasers based on logic, mathematics and paradoxes, as well as wordplay. If wordless crossword puzzles light up your neurons, go to sodukufun.com. You don’t need a large vocabulary to solve these puzzles, just a flair for non-obvious reasoning and an ability to handle changing concepts and perceptions.

For insight into what goes on in your head when you’re solving puzzles and otherwise cogitating, check out The McGovern Institute for Brain Research at the Massachusetts Institute of Technology. Part of the largest neuroscience research center in the world, The McGovern Institute unravels the links between perception, cognition and action and explains them in clear English. A no-brainer!

One route to pain and stress management is greater awareness of your breathing, and unlike aspirins, this is a remedy you’re never without.

Focusing on your breathing to heighten inner awareness has a long history in certain eastern spiritual traditions, and its health benefits are increasingly upheld by western investigators. The Center for Mindfulness in Medicine, Health Care, and Society at the University of Massachusetts Medical School combines the latest psychological findings and the meditative breathing techniques of eastern religions to help chronic sufferers come to terms with pain and lead a more mindful, productive and peaceful way of life.

The Harvard-trained integrative medicine guru Dr. Andrew Weil advocates proper breathing as a tool for self healing. Look into drweilselfhealing.com for more about his “master key” breathing exercises and for free health tips on everything from dieting to back care.

Eyeing a beautiful timepiece can relax even a Type A personality.

The only thing wanting at nawcc.org, website of the National Association of Watch and Clock Collectors, is time enough to marvel at all the timekeepers on display: sundials, flower, cuckoo and grandfather clocks, pocket repeaters and digital chronographs for athletes and divers. Has your vintage wristwatch gone missing? List it here and you may recover those stolen hours.

Trace watch making history from the 13th century to today, at hautehorlogerie.org, the stunning website of a group of Swiss fine watchmakers. Then watch an animation of how mechanical watches and their devilishly intricate mechanisms work. You’ll lose all track of time!

You don’t literally need to stretch your legs to clear your head and refresh your spirit—you can do it in your mind’s eye.

For those times when you feel you’ve reached the end of your tether, snap on the (virtually) real thing at discovery.com and take a sedate excursion in zero gravity to repair the International Space Station. The interactive stroll is based on an actual mission in 2000.

Wander Philadelphia on a self-guided ramble at theconstitutional.com and stop by the Betsey Ross House, Independence Hall and the Christ Church Burial Ground, as well as lesser-known venues such as the B. Free Franklin Post Office. It’s the only active postal center in the U.S. that doesn’t fly an American flag, because a national banner didn’t exist when Ben Franklin became the first postmaster general in 1775.

Feeling down? Return to a buoyant mood with an imaginary dip.

Poolandspa.com ushers you into hot tubs (a Japanese tea house model looks invitingly serene) and diving, lap and negative-edge pools of every conceivable design. Photos of yellow rubber duckies will have you reminiscing fondly about your first swim buddy.

The federal sanctuaries showcased at marinelife.noaa.gov are just the place to set your thoughts gently adrift. Contemplating these coastal, island and undersea parks from Hawaii to Monterey Bay and the Florida Keys is nothing less than restorative.