The Washington International Youth Hostel, the busiest of America's growing chain of 194 youth hostels, will move the next week from a trio of small townhouses at 16th and P Streets NW to a new downtown home, the eight-story, 163-room Franklin Park Hotel, at 1332 I St. NW.

With a capacity of 400, the turn-of-the-century hotel will give the nation's capital the largest youth hostel in the country and the only one in a major city offering low-cost overnight accommodations to members of American Youth Hostels and hosteling organizations in 48 other countries. Hostels cater to young people, especially those hiking, bicycling and traveling on their own.

The new hostel's location, in the heart of Washington's 14th Street topless bar and porno strip, but opposite the recently restored Franklin Park, "has caused some people to say we're crazy," says Robert W. Yeates, executive director of American Youth Hostels.

But the old hotel is four times larger than the present AYH hostel, is downtown close to bus terminals, Metro, cafeterias and tourist spots, and with the influx of hundreds of healthy youngsters and foreign travelers "we see it as the beginning of a comeback for that neighborhood," said Yeates.

The influx began last Thursday when two Australian girls and one French girl arrived in Washington to find the 16th Street hostel full and became the first hostelers to spend the night in the new downtown hostel. Dozens have been placed there since.

The 16th Street hostel, formerly a boarding house for girls, was bought 10 years ago by the AYH national headquarters, with more than $50,000 of its $225,000 cost raised in a citizen fund drive headed by then Interior Department Secretary Stuart Udall.

The Franklin Park Hotel was bought by a member of AYH's national board of directors, Ron Mitchell, because the non-profit AYH was unable to move fast enough to purchase it, Yeates said. Mitchell owns several hostels in Colorado and has agreed to sell the Washington facility to AYH at cost if the organization decides to buy it.

"We want to own a Washington hostel, and the city could use two or three," Yeates said. The money from the sale of the 16th Street building will go into the AYH hostel development fund.

Retired Dutch sea captain Herman Voogel and his American wife, Joan, houseparents at the hostel here since houseparents at the hostel here since 1970, will continue as houseparents in charge of the enlarged hostel.

The 16th Street building has been sold to the Christian Service Corps, which operates a "Christian Peace Corps" and the Christian Inn next door. However, in a complicated land deal, the property is being swapped for 1515 16th Street, which currently is leased by the D.C. Human Resources department as one of the city's two emergency shelters for destitute families with children. Robert Wolpe, of Bethesda, one of the new owners of the youth hostel building, said it will be renovated and be leased for office space and to Human Resources.

The Franklin Park Hotel, where business has been poor since the 1968 riots here, is in good condition and needs only fresh paint, a new kitchen and a new marquee, said Mitchell. Its long-term residents, including a woman there more than 30 years, will be permitted to stay, though residents later may be required to become AYH members (membership costs $5-12 a year.)

Long-tern residents account for about half of the present hostel's occupants, sustaining it during quiet winter months. Initially probably more than two thirds of the new hostel's occupants also will be non-AYH-ers, Mitchell says. The present hostel frequently has had to turn away youth hostel members over the past three years because of insufficient bunk space "and it's a real trick trying to balance the economics of sustaining the hostel and the theory of providing the maximum space for youth hostelers," said Yeates.

The Youth Hostel movement, born in Germany in 1909 as part of an outdoor, back-to-nature movement, has since spread to 49 nations - including many Iron Curtain countries - and now boasts more than 4,500 hostels where traveling members can find a dormitory bunk and communal kitchen in which to make a meal. They include barns, castles, homes, old churches, railroad stations, hotels, a three-masted sailing ship and even a former city jail in Ottawa.

In April two Minnesota congressmen, Sen. Hubert H. Humphrey and Rep. Richard Nolan, introduced the American Youth Hostel Act of 1977. It would provide $9 million in matching grants to renovate old, surplus buildings around the coutnry and develop a national youth hostel system comparable to that in most European nations.

So far, however, the growth of hosteling in the U.S. has been slow, with few hostels outside New England and the Midwest until recent years. Virginia got its first hostel only this month, a summer-only camp of tents and cabins at the Chickahominy Boy Scout Camp, a six-mile bike ride from downtown Williamsburg.

Of the present 194 hostels chartered in the U.S., 81 ar actually motels or hotels, called "supplemental accommodations," which give hostelers a discount but which are still relatively expensive. The Jackson Hole, Wyoming, hostel, a motel in a ski area, costs $13.50 a night, and New York City's hostel is the Prince George Hotel, where even with the discount the overnight charge is $17.

The overnight charge at the new Washington International Hostel will be $4.50 a night, an increase over the $3 charged at the present hostel and the highest charge at any regular AYH hostel in the country. Most U.S. hostels charge about $2 a a night for members, plus a slightly higher fee for non-members permitted to stay a maximum of three days on an introductory AYH pass.

The $4.50 charge is necessary to cover the mortgage, taxes and high operating costs of a downtown hotel - despite its nonprofit status AYH has had to pay taxes on its hostel here - but $4.50 is still cheapr than any place else in town, Mitchell said. The YMCA here charges $12 a night and the Franklin Park Hotel has been charging $15.