TRAVEL ON THE UNDERGROUND. Public transportation can be the easiest and cheap-est way to get around some of the world's major cities including Paris, London and Sydney. If you're adventurous enough to take a self-guided tour of a city, a map with details on how to reach the major sites using public transportation is invaluable. One option is Michael Brein's public transportation maps: "London by the Underground," "Paris by Metro" and "Honolulu & Oahu by TheBus." "Sydney by Public Transit" is due out soon. Each map shows the entire system but lists which line and which stop to use for major attractions. For example, to reach the Rodin Museum in Paris, take Metro (the subway) line #13 and get off at Varenne.

Brein, an Oregon-based travel writer, says the popularity of self-guided travel has generated a broad interest in his maps. "These maps are for all kinds of people on a variety of budgets. There's something satisfying and exciting about moving freely through a new city without the hassles and expense of cabs," he said. "You can move about like you're a local." Each guide is an accordion-style, 4-by-9 inch publication. Each costs $5 plus $1 for shipping and handling. Place a credit-card order by calling 800-875-8083, pin #0026. For more information about the guides, consult the Web at (www.michaelbrein.com).- BOOK SWISSAIR FLIGHTS ONLINE. Switzerland's flagship carrier has a new and improved Web site. The address is (www.-swissair.-com). You can now book Swissair flights and flights on partner airlines including Delta, Austrian Airlines and Sabena (Bel-gium's carrier) and you can reconfirm North American transatlantic flights with the click of a mouse.

- BEST WESTERN HOTELS IN CHINA. Two properties in China have joined the international lodging brand. The Best Western Wanyou Conifer and the Best Western Acorn Inn recently opened their doors. The 332-room Best Western Wanyou Conifer Hotel is a 30-story hotel in the heart of Chongquing. (If you have to ask where that is, you probably don't need to go there.) The property is considered a luxury hotel. The Acorn Inn is also in Chongquing. It's a 60-room hotel. Make reservations for any of Best Western International's properties by calling 800-528-1234. Or visit the Web site at (www.bestwestern.com). Best Western International, based in Phoenix, has nearly 3,800 hotels in 77 countries and territories.

- LOS ANGELES, THE OTHER FASHION CAPITAL. Southern California is the fashion capital of the West Coast. It used to be that only veteran LA shoppers knew the secrets of the fashion district. But now the area, with its eclectic mix of contemporary fashions, jewelry, accessories and fabrics - 50 blocks of retail stores, wholesale outlets and ethnic marketplaces - is something that visitors can navigate. Pick up a map at the fashion district office, 110 E. Ninth St., Suite C625, Monday through Friday, from 8 a.m. to 5 p.m. or visit the Web at (www.dpoa.com).

- SAN DIEGO MUSEUM OF MAN exhibit helps to unravel the mysteries of mummies. "Mysteries of the Mummies" opens July 13 and will run through May 16, 1999. The exhibit includes mummified bodies and hundreds of related relics including caskets, tombs, sacred skills and shrunken heads from ancient Egypt. The exhibit is open daily from 10 a.m. to 4:30 p.m. Admission is $5 for adults and $3 for children 6 to 17 years old. The museum is in Balboa Park, near the San Diego Zoo. For more information, call 619-239-2001, or visit the Web at (www.museumofman.org).

- LEHMAN CAVE TOUR SCHEDULE. Through Labor Day, tours of Lehman Cave in Great Basin National Park will leave from the visitors center at 8:30 a.m., 9 a.m., 10 a.m., 11 a.m., 12:30 p.m., 2 p.m., 3 p.m. and 4:30 p.m. Tours at 11:30 a.m. and 1:30 p.m. will be added Fridays through Sundays. Tours on the hour are 90 minutes in length. Tours on the half-hour are 60 minutes long. Tours are limited to 30 people. You can purchase tickets in advance using a major credit card by calling 702-234-7331. No refunds for advance tickets if you fail to show up on time. Other park activities include a range-led four-mile hike to Bristlecone Grove on Wheeler Peak start-ing at Bristlecone trailhead at 10 a.m. daily.

- THE FRONTIER FESTIVAL at the Buffalo Bill Historical Center in Cody, Wyo., will be July 18 and 19. Events include a pack horse race, horseshoe pitching and a campfire cookoff. The pack horse races will be both days of the festival. The historical center is one of the crown jewels of western museums. It includes the Plains Indian Museum, the Whitney Gallery of Western Art, the Cody Firearms Museum and the Buffalo Bill Museum. The museum is a must-see whenever you're in Cody.

- NEW AT KNOTT'S BERRY FARM. The Supreme Scream open-ed last weekend, the newest attraction at this Orange County theme park. The vertically descending thrill adventure propels you straight up, 252 feet, in midair and then you plunge straight down at more than 50 mph in three seconds flat. The structure is 312 feet high, as tall as a 30-story building. Adventurers who brave this ride are harnessed into outward-facing seats, their legs dangling freely beneath them. The ride was designed by S&S Sports Power, Inc., of Logan.

- SAFETY ABROAD. American Express published a free brochure called "Have a Safe Trip: Tips for the International Traveler." It is available by sending a request to American Express Public Affairs, The Travelers Cheque Group, American Express Co., 200 Vesey St., New York, NY 10285-4815. Among the tips:

- Leave copies of your passport, airline tickets and credit card numbers with someone you trust.

- Never leave luggage unattended.

- Carry only the cash and travelers checks you need for the day.

- Don't resist a robber (what you're carrying isn't worth your life).

- Get a copy of the police report for verification with insurance.