How can I keep my Labrador-mix entertained?

Question

I recently acquired my first dog from somebody who was moving away, but could not take the dog with them. The dog is a 3-year-old Labrador mix. We don't know what the other breed is, but I suspect a pointer.

The dog is amazingly well-behaved. He can "sit" and "shake", he doesn't enter any room unless given permission, he is able to spend a day or so alone, I am able to walk him without a leash, and he will return to me every time I call his name. He is also really kind with small children and friendly in general. When I take him on walks, he really enjoys jogging with me, jumping up on walls, and marking things. He will sometimes also jump up onto me in a playful manner, but very rarely. Another interesting thing I noted is that sometimes he will not eat his food unless either I or my wife stand next to him while eating.

However, I have been unable to get him to play fetch, or tug of war, or much of anything. I tried to buy him a Kong, but he ignores it, or is happy to get one treat out of it and then stop. I got him a chew toy and a rope, but they have been untouched for a week. I'm trying to figure out what sort of activities I can do with him inside the house to keep him entertained. Right now, I have to pet him a lot, or he just sits on his bed. I'm mostly concerned that he will get bored when we are out of the house and get upset, or start to become destructive, or I will have to tie him up in the yard.

I asked his previous owner what he did, and the previous owner told him he just let the dog hang out in the yard, but their yard was much larger than ours and the dog would sometimes run off and then return an hour or so later.

What can I do to get my dog to entertain himself?

Edit: Follow Up

It turns out that my dog does not need to entertain himself. He stays at home and does not ruin anything even when we are out for over 8 hours. (Neighbors come to see he is fed and take him on a walk) He prefers to "play" (going on walks/jogs, being pet, sitting in the same room doing nothing) with people, and not toys, but when alone, he does not appear to have a need to interact with any objects either.

Answer 1

I've had similar issues getting my dog interested in toys. One dog will lay in bed all day and only play on his own "in secret" at night. He is 13-years-old, and historically only interacts well with my wife (his "person"), so I'm not concerned with him. The more universally-interactive dog will not play with toys, but she will sun herself all day. I've recently started a couple activities that she has become interested with and I will relate them here. Both involve a sort of "playful tease"; building her excitement, but not providing her with the toy until she's hit a high level of involvement; a.k.a. "you can't have it."

With both of these activities, I needed to be careful not to get bitten, either accidentally or deliberately (from annoyance). While she is a small dog, she is a dachshund with a powerful bite. She is known to look to me over anyone else for attention, so I know she won't hurt me deliberately. You have a larger dog and must take more care if you try my approaches.

Who's got the Bone?

One act I perform is to get a number of spinal bones from the butcher; these are available at our local grocer, Publix, pre-packaged for dogs. I give her a new bone every week or so. Once she has chewed it clean, I take the bone and sit down at the end of a hallway with her. Then I show her the clean bone, palm it, and ask her over and over, "who's got the bone?" in an excited voice while moving my hand around in the air. Sometimes I shake my hand low and near her. She starts happily jumping in place and shaking and making excited yelp and playful growl noises. This builds up till she starts barking; that's when I toss the bone down the hall and tell her, "GO GET IT!". She'll race after the bone, "catch it", and either leave it be and walk away, or pick it up and prance away with it to chew for a minute. If she's chewing, I either produce another cleaned bone in front of her, or I get the bone from her, and I repeat the process. This can go on for a while; eventually she wears herself out.

The Annoying Plush

She flips over onto her back for tummy rubs all of the time. Recently, while she was on her back, I took a plush toy and rubbed her with it from nose to tail, and circled back and did it again. After several passes of me "deliberately annoying" her, she opened her mouth and tried to playfully bite the toy, following its path over her with her head. This went on for about 5 minutes. I've done it a few more times. Since then, I've noticed a toy has moved from her toy chest a couple times, and I know it wasn't the other dog or anyone else, so it must have been her. This is progress.