Take a virtual museum tour
You can take free, virtual 'walk around' tours of many of the world's most famous museums and art galleries. Wander around the museums of Vatican City in Rome, including the Sistine Chapel, and finish with a tour of Saint Peter's Basilica and Square.
Why not take a tour of the vast and varied collection of London's Natural History Museum, explore the Dutch masters at the Rijksmuseum in Amsterdam, or take 360-degree virtual tours of seven galleries of London's National Gallery, zooming in to see the masterpieces in more detail.
If you set up an audio Zoom meeting on your PC or laptop while you take the tour, you can share the highlights with friends, too.
Paint by numbers
The younger generation has just 'discovered' this perennial hobby, showing off their completed paint-by-numbers masterpieces on Instagram. It's been popular since the 1950s because it's a satisfyingly simple way to get creative, whether you're artistically challenged or more adept with a paintbrush (and there are loads of YouTube clips with tips for best results).
Kits come complete with everything you need - just add patience and the end result is a beautiful painting to frame and display. As a bonus, the focus that such hobbies require is called 'flow', where you're so engrossed that time flies, a state of mind that is great for our mental wellbeing.
You can choose from a wide range of designs, including landscapes and classic masterpieces in a variety of sizes, or send your own photo for a bespoke paint-by-numbers canvas. Try craftyarts.co.uk or masterpiecebynumbers.com.
Join a virtual library
If you're a voracious reader looking for new inspiration, take a wander around a virtual library. You get unlimited access via a tablet or PC to a world of books through Project Gutenberg, a free online book scheme that aims to make every out-of-copyright book available digitally. You can download classic novels from Austen to Dostoyevsky, along with non-fiction bestsellers on philosophy, poetry and religion.
You can also check out Perlego.com for unlimited access to over 300,000 academic titles on everything from architecture to psychology for a monthly subscription. Alternatively, sign up to Cloud Library by bibleotheca, a not-for-profit initiative that aims to offer free access to the digital content of all libraries, including an increasing number in the UK. If your local library hasn't signed up, check out the library's own website, as many now offer free access to digital content.
Knitting has a calming, mood-boosting effect, because it's a repetitive action that uses both sides of the brain at once. If you're not already a knitter, start with a simple project like a scarf, and get virtual help at Bluprint. You can buy wool online at Hobbycraft or Wool4less. If knitting's not your thing, cross-stitching or crochet also has the same effect.
Puzzle it out
Solitaire and Sudoku are firm favourites for putting your brain through its paces (if you're not already hooked, sign up to sudokuweb.org or worldofsolitaire.com). But if you're looking for new brain-training inspiration, sign up to Luminosity for a free memory and brain function test, along with access to online games to challenge your grey matter (from £2.67 a month).
Alternatively, Brain Games has a wide selection of puzzles, crosswords and memory games available for free. Or try jigzone.com for free online jigsaw puzzles. You can also upload your photos to create your own. If chess is more your thing, on chess.com you can play online against a friend or play against the computer, and take part in tournaments.
Learn a language
If you yearn to speak the lingo when you're on holiday abroad, now's your chance. As a bonus, learning a language can stimulate activity in the parts of the brain involved in memory and verbal processing. There are free language courses available from the Open University lasting from four to 24 hours, including beginners' Chinese and Advanced French.
Afterwards, brush up on your vocab with Duolingo, a free app that uses games and point scoring to help you learn the language of your choice. The fun factor is high as it's aimed at children. Or you could try Babbel to learn up to 14 languages with your choice of focus, such as travel, business or culture.
Hit the keyboard
If your piano or keyboard has been neglected since the kids left home, now's your chance to put it to good use and give your brain a new challenge. Choose from a selection of learn-to-play-piano courses on Udemy, from £11.99. Then check out YouTube channels for some free inspiration - try HDPiano, Piano in 21 Days, Instant Piano Genius or the Hoffman Academy.
For a motivation boost, you can sign up for one-to-one online lessons by Skype with a teacher at Music Lessons Anywhere.
Keep your green fingers busy
Do your bit for the environment by learning how to create a bee and butterfly-friendly garden. The online Gardening For Wildlife course is presented by Andy McIndoe, Chelsea Flower Show Gold record holder, in conjunction with the Royal Horticultural Society. You can opt to learn at your own pace or pay a discounted rate to join an online classroom of up to 20.