Discover Utah!...Hub of the western states...The Rocky Mountains for a backbone, the Uinta Range for an arm...15 ski areas, several among the world's finest...

275 public and 100 private campgrounds, ranging from the most primitive, without so much as a ring of rocks for a fire pit, to the most modern, with covered tables and hot showers...more than 3,000 lakes, a third of them fishable, most accessible and with enough boatable surface water to rank it 6th in the country...more than 400 miles of raftable rivers, with parts of the Colorado rated among the country's most challenging...Five national parks, six national monuments, two national recreation areas, one national historic site, six national forests and 45 state parks...10 million acres of high mountain country and probably twice that in sculptured red-rock landscape to the south...

Flaming Gorge and Bear Lake to the north, Lake Powell to the South, the Bonneville Salt Flats to the west, dinosaur country to the east and in the center a potpourri of sights and activities.

Discover Utah? Yes! Not only have Utahns done so, but so have Californians, Bostonians, and Floridians, along with Germans, Britons, Asians, Africans and anyone else with a way to Utah.

Which is why Utahns may find "no vacancy" signs out this summer when they call on favorite recreation areas.

Last year, for example, 7.2 million people visited national parks, monuments and recreation areas, 5.436 million stopped at state parks, and there were 13,977 million user days in the U.S. forests. Nearly 2 million visitors stopped at Zion, and 3 million at Lake Powell. All this was about a 10 percent increase over 1986, and according to early indicators, another big jump is headed for 1988.

Conditions are right, said Joe Rutherford, publicity director for the Utah Travel Council. Gas prices in Utah are low, the dollar in Europe is weak and, most importantly, Utah has appeal.

Translation: It's going to be a busy summer, especially at the more popular spots.

So, a few tips to the locals are: Forget Fridays, stop early and be flexible.

There is not, within the state park system, a Friday open for a large, overnight group camping spot between now and when frost tips the leaves. Fridays are popular with church groups and according to Mistix--the new, private reservation service handling all the state parks and half the U.S. Forest Service areas--are booked solid.

Camping areas can be reserved within 120 days, and according to Mistix, Rendezvous Beach at Bear Lake, Wasatch State Park in Midway, and Black Hawk, a USFS camping area near Payson Lake, are booked. Most parks are also booked for major holidays--Memorial Day, July 4 and 24, Labor Day.

Suggestions from reservation officials are to be flexible when calling, have alternate dates and be willing to switch areas if necessary. Best times to call are early in the mornings and around 2 p.m. The reservation number is 1-800-328-2267

There are no reservations taken at national parks. All spots go on a first-come, first-served basis. Consensus at the various parks is that if you want a camping spot, check in before noon.

"The usual pattern," said Bill Miles of Bryce National Park, "is campers get up early, take a few pictures and are out by lunch. If people arrive early, and there are no campsites, we suggest they go see a few sites, then come back. "Miles said that throughout the summer, Bryce's 220 campsites are filled by evening.

Victor Jackson, chief park naturalist at Zion National Park, also said visitors that want camping spots should check in early. "We tell people to be here before noon. After six, on any given day the chances are very slim," he added. There are 375 campsites at Zion.

This year, it is expected Zion will be seen by 2 million visitors. Last year was a record, and this year, through March, figures are running 15 percent ahead of last year. According to Jackson, groups can make reservations "such as the Boy Scouts and church organizations, but not for family reunions."

At Canyonlands, reported Betty White, when the campsites are filled, visitors can move onto adjacent BLM lands and camp. "There are no facilities, though, none at all," she added.

If all the camping areas inside a park are taken, travelers should consider staying in one of the nearby towns.

One of the state's most popular stopping-off spots is Lake Powell. This year, more than 3 million people are expected to visit one of the five marinas.

Accommodations there include houseboats (307 lakewide), lodge rooms (294 at Wahweap and 45 at Bullfrog), and campsites. Harde3st to get are the houseboats. They are, on paper anyway, booked.

"but, that doesn't mean people can't get a houseboat this summer," said Dick Kemp, director of public relations and advertising for Del E. Webb Recreational Properties. "Problems come up and people do cancel...Up to 30 days before the reservation date and they get their money back.

"So, we suggest calling 30 days before you want to go and checking on cancellations. And remember, every day is a new 30 days. If I really wanted a boat, I'd call often. Also, ;you can put your name on a waiting list. Just ask how many are on the list, and you can see what your chances are."

And there are alternatives to houseboat living on the lake. Kemp suggested staying in one of the lodges (Wahweap or Bullfrog) or trailers (Hite and Halls Crossing) and renting a smaller powerboat to tour and recreate on the lake. "And there are," he added, "some advantages to doing it this way."

Also, there are campsites for RVs reserved through Bullfrog and Wahweap, as well as national park sites at each marina to go with the rental of smaller boats.

In U.S. forests, Mistix is handling reservations for group areas in Uinta, Ashley and Wasatch/Cache forests, and half the individual areas in the Uinta. Other spots are on a first-come, first-served basis. Other forests are handling reservations directly, noted Kathy Pollock, public information assistant for the Wasatch/Cache unit.

Here, also the suggestion is to be early--weekdays between 7 and 9 a.m.; for weekends be there early Friday, or arrive late Saturday or early Sunday, and for holidays plan on getting to a spot two days early. And, as with the state parks, an open Friday for group areas this summer is almost impossible to find.

The bottom line is that if you are among those planning a summer outing, plan ahead, be flexible and move in early.