About 5 years ago I found a fanny pack (lol) with $700+ cash in it on the NYC subway. There was no ID, but there was a small personal phone book with a woman's name in the "this belongs to" slot. I looked up someone with the same last name in her phone book and called to say I had found the money. It was her son, who gave me his mother's address and I ended up taking the train out to the far reaches of Brooklyn to return it to her.
Turns out she was ~80 years old and the money was for her annual trip to Atlantic City that she saved all year for. She was sobbing she was grateful I returned it. I know if I had turned it into the MTA lost & found she never would have gotten it back. I'm hoping that earned me some serious good karma, since at the time I was pretty broke and really wanted to keep it.
Awww!...I'm so glad for that woman that you found the money, that is such a sweet story.
I would have told the manager that I found some amount of money, given him my number, and taken it with me. Then I would have returned it to the person who called with a legitimate story and who knew the amount of the missing funds...
As for traveling out of state, you could always send a check or money order...