My husband was deeply involved in Big Brothers before we married, and I know he felt his time was a valuable gift to the kids he worked with. He also was a Boy Scout for 52 years and did much the same thing with the boys in his troop whose dads were serving overseas. He would generally set up an activity, such as going bowling or going hiking, and then he and the kid would do this together. Thus there was something to do but also plenty of time to just talk if needed.
Since my husband is now disabled and unable to do all the “guy things” with our son, we contacted Big Brothers Big Sisters to try to find a Big Brother for him. They were very nice and very thorough in their interview process. Unfortunately, the demand for Big Brothers is far greater than the availability, so we have never been able to get assigned to one.
However, we are doing a similar thing through our church with what we call a “loaner Dad.” About once a week he will call in advance to be certain what he plans to do meets with my approval and fits in our schedule, and then he will come get my son for the activity. Once he took my son on a fishing boat, once to go SCUBA diving, and last weekend they just hung out and worked on his car. Next week they are supposed to go out in the country and ride ATVs (and probably spend a lot of time fixing them), which is something my son is really looking forward to doing.
Sometimes sports coaches fill a similar role, especially in leagues that cater to the lower income kids. My son was also in the baseball program put on by the Salvation Army and the Police Athletic League. That coach was terrific with the boys and even had extra events outside of practice and games. He took the team to Fiesta Texas and held several barbecues for them. He also holds study sessions in his living room. Generally, the guys who do this best are ones who grew up poor and/or without a dad, but have managed to be successful in spite of their hurdles.