In countries that don’t accept U.S. currency, I recommend exchanging money at a local bank if possible, followed by a local exchange shop with good exchange rates. I have found the hotel and airport exchange shops to have the highest exchange rates, but the airport shops are safe and handy in a hurry. Shop around for the best rates, but don’t let the search take time away from your vacation!
Use pickpocket-proof clothing and bags. And don’t overlook the small safe now common in most hotel rooms. Finally, while it may be cheaper or more fun to use the subway (such as Tokyo's elaborate subway system), a cab may be safer.