The completion of I-66 doesn't just promise to get you more quickly to where you have to go every day. It also could get you thinking about new places to go to that you thought were too much of a hassle to get to before.

Take, for instance, Skyline Drive, which as of today is suddenly about 75 minutes from the Potomac, instead of what used to be an 90 minutes and up. Or Fauquier and Loudoun counties' Hunt Country, with all its spectacular estates and prize-winning vineyards and country inns. How does 45 minutes away sound?

As for you suburbanites, how about the fact that, with the mere snipping of a ribbon, many of you are abruptly within minutes-- literally--of the Mall and all its museums.

It should now take just over 12 minutes, at an average speed of 50 miles per hour (the speed limit will be 55 mph), to drive the 10.1 miles from the Theodore Roosevelt Bridge to the I-66 interchange with the Capital Beltway.

Compare that with the stop-and-go 20 to 30 minutes it now takes to drive the 10.84 miles from the bridge to the same interchange via Rte. 50 and the Beltway.

Here, aside from downtown Washington, is what you can get to easily via a completed I-66:

* Historic Fairfax County Courthouse: Just a few miles south of I-66 on Rte. 123 is the courthouse where the wills of George and Martha Washington are kept. There is also a memorial to Capt. John Quincy Marr, the first Confederate killed in action. Col. John S. Mosby and his famous Raiders left hoofprints all over the neighborhood. For information, call the clerk's office at 691-2224.

* Sully Plantation: About five miles north of I-66 on Rte. 28 is another landmark, Sully Plantation, built in 1794 by Richard Bland Lee, Light Horse Harry's brother and Robert E.'s uncle. Lee, a delegate to the First Continental Congress, founded Phi Beta Kappa and is generally considered responsible for the nation's capital being on the Potomac. For information, call 437-1794.

* Bull Run Regional Park: Located a few miles south on Rte. 28 at the edge of Fairfax County, this park offers 2,576 acres for camping, hiking, skeet shooting and swimming. It also has a marina because it borders the 16-mile-long Occoquan Reservoir, which is kept stocked for fishing. The park's summer Country Jamborees and annual reenactments of the First Battle of Bull Run attract as many as 20,000 spectators. For information, call 278-8880.

* Manassas National Battlefield Park: Just to the west of Bull Run Regional Park in Prince William County is the site of the first battle of the Civil War. Actually, two separate bloody battles were fought here, and together they generated casualties of nearly 24,000 soldiers. For information, call 591-3275.

* The tiny town of The Plains: A few miles northwest of I-66 on Rte. 245, in Fauquier County, is the old country village called The Plains. This is a potential I-66 success story. At first, it seemed that the coming of I-66 was the death knell for The Plains, which until then had squatted astride the only major east-west highway, Rte. 55. In fact, however, the building of I-66 has proven a blessing. A transfusion of cash has revived it, with multimillionaire Arthur W. Arundel's The Plains Village Trust responsible for the restoration of a dozen historic buildings in the middle of town and the recruitment of new businesses to fill them.

* Hunt Country: The Plains also serves as a gateway to horse and Hunt Country, where fox hunting is the passion of the wealthy. Middleburg (north of The Plains on Rte. 626) is Hunt Country's capital. Picturesque and filled with shops, it also offers some good eating spots, like the Windsor House (703-687-6800), where such English treats as Pimm's Cup and Yorkshire pudding are part of the menu.

Meanwhile, Middleburg's Red Fox Inn (703-687-6301), established in 1728, recalls our more political past: In 1883, Col. Mosby came to the tavern to meet J.E.B. Stuart. Some 75 years later, Sen. John F. Kennedy gathered the press upstairs to announce his presidential candidacy. West toward Upperville is Welbourne (703-687-3201), a magnificent private home with rooms and cottages to rent.

* Upperville: This Hunt Country town boasts not only one of the country's oldest horse shows but perhaps the one of the most elaborate reproductions of a medieval European church in America. Trinity Episcopal Church, commissioned by Paul Mellon and constructed by imported craftsmen, reproduces the 12th- and 13th-century architecture of Norman country churches.

The opening of I-66 also provides convenient access to Virginia's wine country. The gold medal-winning Meredyth Vineyards at Stirling Farm lies between The Plains and Middleburg off Rte. 626 (Washington-area phone: 471-4399). The Piedmont Vineyard of Mrs. Thomas Furness is three miles south of Middleburg on Rte. 626 (703-687-5134). The Robert Harpers' Naked Mountain Vineyard is 1.7 miles north of Markham on Rte. 688. Farfelu Vineyard is south of Marshall on Rte. 647 in Flint Hill.

* Skyline Drive: Almost at the end of I-66 are Front Royal and the entrance to the 105-mile Skyline Drive and its waltzing partner, the Appalachian Trail. For information, call 703-999-2266.

* Strasburg: At the very end of I-66, where it joins I-81, is Strasburg. The Old Mill (703-465-5980), built about 1775 and now a restaurant, supposedly was spared during Sheridan's torching of the Shenandoah Valley, thanks to the amorous exploits of the miller's daughters with the general and his officers.