Staying in the US?

Even as Europe braces for a summer invasion by that wide-ranging species, Touristus Americanus, it appears that a good number of travelers will leave their passports and phrase books at home to fan out across the United States.

All signs point to revived touring patterns in the US, according to Arnold Fury, manager of travel programs for Mobil Oil and the editor of the Mobil Travel Guides. ''Things are shaping up very well,'' said Mr. Fury from his Fairfax, Va., office the other day. ''Most people - 80 percent or better - use the auto when they travel, and the good news for them is that gas is stable, or even below prices of a year ago. Also, because the economy has been soft, there is an abundance of good deals to be found out there.''

Mr. Fury included in this abundance the coupons one can clip from a Mobil Travel Guide to a particular region, offering reductions of 10 to 50 percent for six hotel chains and any number of attractions, from the Baseball Hall of Fame at Cooperstown, N.Y., to Sea World in San Diego.

He said that while national parks and theme parks suffered through recent travel-thin summers, they are due for promising seasons in '83. As for what strategy the American highwayman should use in the coming summer, Mr. Fury advised:

''Travel early in the day to avoid the afternoon heat. This will mean less traffic and less air conditioning, thus lower fuel costs. Avoid traveling on weekends when everyone else goes on the road. Try to do the bulk of your driving during the week.''

While it appears that air fares will be comparatively better abroad than at home (transatlantic fares are actually down from last summer), there are still Super Savers worth booking to various points in the US. Most call for a 7-day advance purchase and stays of 7 to 14 days. United Airlines recently came out with a different version of the Super Saver that, while not as low-priced, provides a much longer stay, up to 60 days - almost, in other words, a full summer.

Summer may be defined by some as school's-out to school's-back or the life span of a bathing suit, but for me it runs from the Spoleto Festival USA in late May to the Pendleton (Ore.) Roundup in mid-September. Spoleto, scheduled this year from May 20 to June 5, perennially ushers in the first sultry summer heat of the South Carolina low country. Charleston is both stage and backdrop for the lively series of arts performances and exhibitions.

Spoleto weekend package tours can be had by writing PO Box 704, Charleston, S.C. 29402. Hotels in the area help promote the 16-day festival, and these range from the luxe, such as the Sheraton Charleston and the Mills House, to the economical, like the private homes and carriage houses that are part of Historic Charleston Bed & Breakfast; (803) 722-6606.

On the way to Pendleton, which this year erupts from Sept. 14 to 17, are scores of fairs, festivals, and annual events worth dropping in on. Philadelphia , proving you don't need a round number to have a birthday celebration (like the Brooklyn Bridge's 100th) is trying to draw visitors to its 301st. Shakespeare theater is scattered all across the land and, in fact, around the calendar. In addition to the well-known Shakespeare festivals at Stratford, Ontario, and Stratford, Conn. (recently rescued from the brink of financial ruin in time for the '83 season) there are smaller fetes at Ashland, Ore., hard by the Rogue River, to the end of October; at High Point, N.C., from mid-July to December; at Cedar City, Utah, a short drive from the equally dramatic Bryce and Zion National Parks, from mid-July to late August - and no doubt a few I haven't heard of.

Summer is also the time to visit places you'd only think of going to in the winter. And I don't mean Death Valley. Two of Florida's grandest dames, the Breakers at Palm Beach and the Boca Raton Hotel and Club, 22 miles south, lower their prices by up to 40 percent in the off-season to try to fill their sumptuous rooms.

The Breakers, one of three US hotels to win five stars from Mobil and five diamonds from AAA, makes its 1926 Italianate splendor available for $65 a day for two (and no charge for kids under 12 sharing their parents' room). Boca's Moorish air, not to mention its 22 clay courts, marina, and golf course, can be had for $90 to $150 MAP (two meals) per day from June 1 to Sept. 30.

Summer isn't a particularly economical time to ride the rails (most of the bargain fares are offered in the laxer months), but those who do will encounter fewer overheated and stalled cars than at any time since Amtrak was born in 1971 . New and refurbished equipment is also improving the on-time record steadily. And as of April 25, Amtrak had a glorious new route - at least on paper.

That was the day the California Zephyr was supposed to begin running from Denver, through the Rockies and across the Wasatch Range en route to Salt Lake City and Oakland. But massive mudslides in eastern Utah have forced Amtrak to divert - but only temporarily - to its former route across southern Wyoming.

One of the high points, in more ways than one, of the scenic new run will be the circuit of the six-mile-long Moffatt Tunnel just before Winter Park, Colo. It's the longest tunnel and the highest elevation on Amtrak's system. It may be one of the few places to keep the American traveler in the dark during the bright summer ahead.