I have an Android phone and I use the free sudoku from genina.com
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Shwmae Simon, diolch for asking, you have given me an excuse to prattle on about games. 
I play for critical problem-solving, visual-spatial coordination, and for reflex. And for me, it is immensely relaxing, so I use it as a means to destress. It’s also inexpensive in the long-term. I buy games from £1 to a maximum of £10. This provides a few months of play, sometimes more. There are also lots of free games and demos, so one is really spoilt for choice.
If you are intending to use the paddles for upper limb rehab, you would probably be looking at games that utilise the paddle’s motion sensors as part of the gameplay. These would most likely be more action orientated games, but still fun. Not my cup of tea, but I wouldn’t be surprised if there are boxing games that would provide some pretty rigorous upper limb rehab. The closest game I have to that genre is ARMS which is a relentless and ridiculous fighting arcade game.
I usually purchase two games at a time, one for problem-solving and the other as gratuitous action. This serves whatever mood I’m in. So, for instance, I would play FAR: Lone Sails for problem-solving, and Jet Kave Adventure for running around, hitting things. I was a child of the point-and-click game generation, so I often will preference these for problem-solving, and they bring back a warm, fuzzy, nostalgic feeling when I sit down to play.
The great thing about the Switch is that it is portable. You can play it on the telly screen which I prefer, but if inclined you can take it out with you. It’s pretty rugged too.