We asked a panel of our most experienced senior travelers to come up with the answer. They chose: Las Vegas NV, Tucson AZ, Philadelphia PA, Los Angeles CA and Atlanta GA. Not necessarily in rank order, here are their choices:

1. Las Vegas NV: This could be a surprise to some people who haven't yet been to Sin City. They believe Vegas is there just to take your money in the casinos, and they're right if you go just to gamble. However, if you visit Vegas to enjoy all the many other pleasures the town offers, you'll be amazed at how easily you can do it on a budget.

Hotel rooms and suites at the best high-rise resorts that would cost you $800 a night in New York City are less than $100 in Vegas. The famous Vegas buffets and dinners with price tags of $10 would cost $50 or more in Chicago.

Some Vegas hotels offer bargains at $100 a night that include unlimited free buffet meals each day. Serious chowhounds can easily scarf up the cost of the room.

Stroll the Vegas Strip and old Wild West downtown area and enjoy enough free entertainment to keep you happy for hours. The Fremont Street Experience is a huge nightly overhead projection video show. 

2. Tucson AZ: Once a sleepy little desert town, today it's a modern city of a million people. It still offers the classic Arizona desert beauty that budget-minded tourists love. Surrounding Tucson is the magnificent Saguaro National Park, where the tall cacti rule the landscape.

Stroll along with rattlers, roadrunners, coyotes, pumas and javalinas. Hotel and restaurant prices are modest by big city prices, and the summer warmth lasts all year long.

3. Philadelphia PA: Visit the colonial city where the U.S. was born in 1776. Hotels near Independence Hall are reasonably priced, except during holidays. Many restaurants, department stores and fine shopping are all within walking distance. Fairmount Park and the banks of the Schuylkill River are great for boating, cycling, strolling or picnics.

4. Los Angeles CA: See the great sights of Hollywood, Beverly Hills and the beaches of Venice and Malibu. Along with touring and hiking, experience amusement parks and budget oceanside restaurants. While shopping in Beverly Hills, you may bump into favorite stars also looking for bargains.

Get free tickets to live TV or tapings at studios and theaters. Great museums and galleries, many with mid-week free entry. When you tire of hiking and biking, extensive Metro bus and subway service costs just $5 for an all-day pass.

5. Atlanta GA: It's the biggest airline hub in the world, so if you're flying from here to there and must change planes in Atlanta, take the time to spend a day or two in this wonderful town. Ride a bus to the enormous carving on Stone Mountain, featuring massive figures of Confederate heroes.

Ride a tour boat or rent a canoe along the Chattahoochee River. See for free the Fernabank Science Center and Governor's Mansion. Also the Jimmy Carter Library and Museum and Martin Luther King National Historic Site.

Of course, there are many more than just five great American cities to visit on a budget. If you do online homework before you go, you'll find bargain prices for hotels, restaurants and entertainment in almost any city.