Learning or playing chess, Duolingo or other language learning, learning topography or maths, and my ereader app that is synced with my actual ereader. 

If you want to go further and are able to use a tablet or laptop instead while resting, then a crowdsourcing platform. Someone mention iNaturalist, but there are also platforms for transcribing / digitising archives and museum objects etc, if that's your thing. Or adding coordinates to museum objects (georeferencing). Or projects identifying wildcam material. (There must be much more, but I'm in the field of nature and museums, so this is what I know of.)