TRAVEL BARGAINS : SWISS JOURNEY INCLUDES TRAIN RIDE TO ST. MORITZ.

Byline: Daily News

An eight-day, seven-night package offered by Basel Tourismus includes sightseeing in two Swiss cities starting at $563 per person. The Herzl package includes four days in Basel, which borders France and Germany on the Rhine, a train ride into the Alps, and four days in St. Moritz, an international ski mecca for four more days. Air fare to Switzerland is not included. Information: [phone].

Discounted stay: At 60 Hyatt hotels in the U.S. and Canada from Dec. 13 through Jan. 4 (excluding Dec. 31), room rates will range from $49 to $69; at 18 more Hyatts, room rates will range from $79 to $119. Information: [phone].

Go Greyhound: Through Jan. 31, with a 21-day advance ticket purchase, Greyhound Lines offers special rates to any of its 2,400 destinations. Bus tickets cost $59 one way and $119 round-trip; also available is a $79 one-way and $158 round-trip offer for passengers who purchase tickets 14 days in advance. And with a three-day advance purchase, Greyhound's ``Friends Ride Free'' program allows two people to travel for the price of one through the end of January, and children age 2-11 can travel free through Dec. 15 with an adult who purchases a one-way ticket through Greyhound's ``Kids Ride Free'' program. Blackout dates for all programs are Dec. 18-24. Information: [phone].

Senior stays: Through 1997, the Holiday Inn SunSpree Resort Lake Buena Vista and Holiday Inn Hotel & Suites Main Gate offer Decade Discount senior savings that increase with a guest's age. Seniors must be 50 or older to qualify. Room rates begin at $70 per night at Lake Buena Vista and $65 at the Holiday Inn for guests age 50-59 down to $30 per night at Lake Buena Vista and $25 per night at the Holiday Inn for guests age 90-95. Guests 100 or older can stay free up to seven nights at both hotels. Information: Buena Vista, [phone]; Holiday Inn, [phone].

Your own cottage: Accommodations in Britain are offered for as little at $23 per person per night - based on six people sharing a cottage - by Country Cottages Inc., which offers privately owned cottages, townhouses, manor houses and castles for rent. Rental rates per cottage per week (the minimum rental period) through December 1997 range from $559 to $955 for a one-bedroom home, $783 to $1,188 for two bedrooms and $953 to $1,346 for three. Information: [phone].

Fly and drive: For travelers who hold an El Al round-trip ticket from the U.S. to Israel for travel through April 30, the airline offers a rental car with unlimited mileage for seven days at costs starting from $7 for a car with a manual transmission or $84 for an automatic transmission. Gas and insurance are not included. Car upgrades and additional days are available at discounted rates and must be purchased before leaving the U.S. (A $15-per-day supplement is charged Dec. 20-Jan. 5 and April 12-30.) Information: [phone].