I use my handheld geocaching GPS (with maps loaded) for walking around in cities, too. Garmin has maps available for all over the world, including a line called City Navigator for various cities. (Maps for the whole US, Canada, and Puerto Rico run about $100, for example.) All you have to do to find your way back to your hotel is to have it marked in your GPS before you leave. Then you just navigate back to the original point. It takes you turn by turn, just like the car version. And I've never once walked into traffic while looking at it! It runs on regular AA batteries, which last several days of constant use, more if you use it sparingly, so I never have to worry about recharging it or having it run out of power in the middle of my day.
GPSs for such purposes (as well as for hiking and outdoor activities) come in all price ranges. The lower end ones can't use maps, however. Please PM me for more information - I'd be happy to tell you more.