I highly recommend the LL Bean Healthy Back Bag. It fits over 1 shoulder and stays in place. It comes in a couple of sizes to suit your needs. My DH usually carries a small, traditional backpack, but its a pain to get on and off. I just purchased a Baggallini Bon Voyage Bag to use on our cruise. I'm going to test it next month when we go to Tampa for the weekend. It looks like it should hold everything including our digital camera, passports,cell,and my girlie junk.
Just a suggestion, when you do purchase your bag and before you remove the tags, fill it with everything that you would carry in the parks. Carry it around the house for awhile and see how it feels. In other words, give it a test run.