Call them up, inform them I found it (if it has a phone number inside anywhere) and then bundle it up and mail it on. A person's wallet is just like their purse or cell phone, in my opinion. We store so much information in there that is often very difficult to replace or downright impossible. The cash inside is the least of somebody's concerns these days, more than likely. Most people don't carry large sums of cash anymore, but the credit cards, certifications people carry, licenses, and all else means that when they get their wallet with all cash returned inside, they know that the person returning it was "a good person", so they won't worry so much about having their identity stolen or their credit cards saved for later usage. It's the peace of mind that will be most valuable to people, I would think.
Edit: Though my first reaction is to mail it to the address on the ID, as I think about it for another 10 seconds, I realized something: It is fairly common for people's address on their wallet to be out of date, at least around here. I've often picked up patients off the side of the road, and when bouncing their information from their ID off of them, they've told me how they moved years ago, and the license hasn't updated yet. Since NY licenses expire very infrequently, it's not an uncommon occurrence. Perhaps sending it forward to the cops would be best, as they would stand a better chance of tracking the person down. Though, knowing my own local police force and how relatively limited their resources are... I think I'd actually try to track them down on Facebook in the end. Try to find the name of the person online, match the picture to the picture on the ID, and then ask the person to verify the address on the license.