Volunteer with the kids and add to the list of things to do with them while teaching them valuable lessons at the same time.
There are all sorts of ways a stay-at-home dad can involve the kids by giving back to the community, and the benefits are never-ending. Volunteering will teach them that it is good to help others, help lessen a sense of entitlement and give them even more quality and fun time with dad.
Take the young ones along on a Meals on Wheels run or to visit elderly people in nursing homes or assisted living centers (but check with program directors first to make sure it is OK). For older kids who are able to help out at soup kitchens and similar charities, let them help dish out meals or clean off tables with you.
Let the children pick out old toys and clothes to give away and then take them to hand deliver them at a chosen charity. At home have the children brainstorm ideas on how they can give back and let them make a volunteering plan.
Most of all, be creative, have fun and help out others at the same time. Volunteering can be a pretty good and different way to spend a day with the kids while staying at home.