Ask him to drive you to your doctor's appointment or to wait in the
waiting room (or even to go in with you if you are anxious about your visit, and
already trust him).
Attend religious services.
Attend a funeral.
Spend a Saturday afternoon volunteering together (taking a homeless
child to a park or working at a soup kitchen).
Go shopping together. Men traditionally don't like shopping, but they do
have to do it some time or another. Choose something that he needs or enjoys,
such as even shopping for a new computer. Consider window-shopping, even if you
are not prepared to buy right now.