NOT LONG AGO when the world was young, two kids took a ride to a cabin in the mountains. They drove her 1967 Volkswagen, whose engine he had rebuilt after it ate an exhaust valve on Michigan Avenue NE. The air-cooled bugs were rough on valves, particularly in No. 3 cylinder where the oil-cooler column blocked ventilation. No. 3 always seemed to run hot.

The deal was he rebuilt the engine and in return she cleaned up his apartment, which was a bargain for him. But they both were pleased, and in celebration they scheduled the trip and leased a cabin near Gettysburg, Pa., from the Potomac Appalachian Trail Club.

The fee back then was $3 a night, if memory serves, but they had to agree to welcome into their temporary abode any hiker who happened along the Appalachian Trail, and as the VW ticked along the highway they wondered how that might work out.

The cabin was a short hike from where they parked, and they lugged their gear through the crackling leaves. It was early spring; only the willows hinted green.

The cabin was rough, like all 12 PATC cabins open to the public. It had a stone fireplace and a wood cookstove. There was plenty of wood around. You drew drinking water from a spring and the lights were kerosene lamps.

They went for a hike, then built a roaring fire and drank hot chocolate in front of it. They were planning to sleep upstairs in the loft, where the bunks were, but it got cold. He suggested they put a couple of mattresses down in front of the fire. It was quite a weekend.

Early this spring these people went to a cabin in the mountains again. This time it was in Syria, Va., at Graves Mountain Lodge, where some friends were waiting for them in the big Lower Cabin, which sleeps 17.

It was raining hard when they left town, and the passenger-side windshield wiper kept falling off. He had to get out and fix it in the rain. The dog was curled up under her feet and the kids were in the back shouting at cows, sheep and horses. Throw in three bags of food, four sleeping bags, a duffel, two carry-ons, a camera bag, snack bag and the little cooler, and there isn't much room left in a diesel Rabbit.

When they got to the big cabin it was still early and no one inside heard them coming. The tin roof was shiny wet and March rain dripped off the front porch gutter.

They gathered up gear and clambered up the steps. He threw open the door. Their friends were clustered in a half-circle, all the chairs drawn up close to the big stone hearth in the orange glow of a well-built fire.

"Home," he thought.

Potomac Appalachian Trail Club still maintains 12 rustic cabins for public use, as well as six for members only. Seven of the public sites are in Virginia, three in Pennsylvania, one in Maryland and one in West Virginia. Only two are more than 115 miles from Washington.

The rates remain ridiculously low, although you need a master's degree to figure out the rate structure, which includes guarantees, minimums, reservation fees and penalties for no-shows. Basically it's $3 a night per person for nonmembers, $2 per person for members.

These are wild and rustic cabins with no modern conveniences, and require a walk-in. Parking areas lie anywhere from 20 yards to 31/2 miles from the cabin sites.

For information, write PATC, 1718 N St. NW, Washington, D.C. 20036, or call 638-5306. CABINEERING

There are plenty of other nice rental cabins around, some public and some private. Here are a few that come highly recommended:

LOST RIVER STATE PARK -- 120 miles from Washington in Mathias, W. Va., has 24 cabins -- nine deluxe and 15 standard -- ranging from $145 to $255 a week, or $21 to $75 a night. Call 800/624-8632 or write Lost River State Park, Mathias, W. Va. 26812.

GRAVES MOUNTAIN LODGE -- about 100 miles from Washington in Syria, Va., has six cabins and a range of fees, many including meals at the lodge, plus a dormitory and two hilltop motels. Write Graves Mountain Lodge, Syria, Va. 22743 or call 703/923-4231.

CACAPON STATE PARK -- about 85 miles from Washington in Berkeley Springs, W. Va., has 30 cabins (11 deluxe, 13 standard, six economy), fees from $165 to $255 a week, or $21 to $65 a night. Call 800/624-8632 or write the park in Berkeley Springs, W. Va. 25411.

SMOKE HOLE LODGE -- about 175 miles from Washington in Petersburg, W. Va., is a big vacation cabin on the Potomac accessible only by canoe or a 90-minute four-wheel-drive voyage over the mountain. Write Smoke Hole Lodge, Box 953, Petersburg, W. Va. 26847. And here are some that come untested, straight from the book "Lodges and Cabins," by John Thaxton ($8.95, Burt Franklin and Co., 235 E. 44 St., New York 10017):

MARYLAND

ELK NECK STATE PARK -- nine cabins overlooking Elk River at the top of Chesapeake Bay. Write 4395 Turkey Point Rd., North East, Md. 21901 or call 301/287- 5333.

HERRINGTON MANOR STATE PARK -- 20 cabins near a lake one mile from the West Virginia line. RFD 5, Box 122, Oakland, Md. 21550 or 301/334-9180.

NEW GERMANY STATE PARK -- 11 cabins in a piney wood in far western corner of the state. Route 2, Grantsville, Md. 21536 or 301/895-5453.

VIRGINIA

WESTMORELAND STATE PARK -- 31 cabins on the Potomac River below Morgantown Bridge, 60 miles from Washington. Route 1, Box 53-H, Montross, Va. 22520 or 804/493- 8821.

SKYLAND AND BIG MEADOWS -- in Shenandoah National Park offer lodge and motel-type rooms and some cottages about 100 miles from Washington. Write ARA- Virginia Skyline Co Inc., Box 727, Luray, Va. 22835 or call 703/999-2211.