If the World's Fair in Knoxville, Tenn., isn't on your vacation itinerary, here are seven of the biggest state and county fairs nearby, all of them worthy of a one- or two-day trip:

* Montgomery County Fair (16 Chestnut St., in Gaithersburg; I-270 to Montgomery Village Exit, south on Route 355 to Chestnut), tomorrow through Saturday: livestock judging; horse shows; 4-H and home arts exhibits; a cheese "extravaganza"; antique farm machinery display; country music show Saturday at 7 p.m.; and carnival. Gate fee, $3; ages 10-15, $1; under 10 free; parking, $1.

* Maryland State Fair (exit 17 off I-83 at the Maryland State Fairgrounds in Timonium, just north of the Baltimore Beltway), Aug. 28-Sept. 6: Acres of farm, home and garden exhibits; livestock at the Cow Palace; race-track betting; horse shows; a large carnival. Gate fee, $2; 12 and under free.

* Virginia State Fair (Laburnum Avenue at Richmond-Henrico Turnpike in Richmond), Sept. 23-Oct. 3: 11,000 exhibits, 5,000 head of livestock, 1,000 horses; 80 shows and rides on the midway; nightly fireworks. Advance one-day tickets, $4.95 (entrance, grandstand, all rides and exhibits) from Crown gasoline stations in Virginia until noon Sept. 22; at the fairgrounds, $6.95.

* The Great Frederick Fair (Frederick Fairgrounds at I-270 and I-70 in Frederick, Md.), Sept. 21-25: It bills itself as the "last fair in western Maryland," third in size behind the state fair and Montgomery County's. Harness racing, agricultural exhibits and livestock, carnival; Roy Clark in the grandstand for two evening shows on Sept. 22; demolition derby on Sept. 23; Fantasy on Wheels, a daredevil show, on Sept. 25. Gate fee, $2; 12 and under free; $1.50 per car additional.

* West Virginia State Fair (on Route 219 in Fairlee, just south of Lewisburg near the Virginia state line at Covington), now through Aug. 28: harness racing, horse shows, free circus, 10 acres of rides and midway shows; grandstand entertainment featuring Roy Clark tonight and Barbara Mandrell on Wednesday; nightly fireworks. Gate fee, $2.50; 12 and under free. Booklet of 50 tickets for rides, $10.

* The Great Allentown Fair (17th and Chew streets in Allentown, Pa.), Aug. 31-Sept. 6: One of Pennsylvania's biggest with a heavy emphasis on the state's ethnic heritage. A different national festival daily, beginning Sept. 1, featuring in sequence the food and music of the Germans, Slovaks, Hungarians, Polish and Ukrainians. Gate fee, $2; 12 and under free. $3 for unlimited carnival rides.

* York Inter-State Fair (334 Carlisle Ave. in York, Pa.), Sept. 10-18: Another big one, it claims to be the oldest agricultural fair in the country, dating its origins to 1765 (with a lapse from 1815-1852). Popular for its ethnic food stands, featuring Pennsylvania Dutch dishes, sausage sandwiches, fried mushrooms and barrels of pretzels. Harness racing and carnival midway. Gate fee, $2; ages 6-12, 50 cents; under 6 free.

And five smaller county fairs for a few hours' visit:

* Shenandoah County Fair (just off I-81 in Woodstock, Va.), Aug. 29-Sept. 4: livestock; homemakers displays; small carnival. Gate fee, $2; under 12 free.

* Fredericksburg Agricultural Fair (on Route 2, two miles south of Fredericksburg, Va.), Sept. 2-11: horse show; tractor and 4-wheel truck pull; homemaking and handicraft displays, small carnival. Gate fee, $3; under 12 free; parking, $1.

* Anne Arundel County Fair (Sandy Point State Park, Md. off Route 50 at the Bay Bridge), Sept. 16-19: livestock and agricultural exhibits; small carnival. Gate fee, $2; ages 9-12, $1; under 9 free.

* Charles County Fair (3 miles south of La Plata, Md. off Route 301), Sept. 16-19: daily 4-H and Future Farmers of America demonstrations; livestock; small carnival. Gate fee, $2; 12 and under free.

* St. Mary's County Fair (just south of Leonardtown, Md. on Route 5), Sept. 23-26: 4-H livestock and homemakers exhibits; greased pole contest on Sept. 24 at 4 p.m.; grand parade Sept. 25 at 11 a.m; 4-H and Future Farmers livestock auction, Sept. 25 at 4 p.m.; small carnival. Gate fee, $2; ages 6-16, $1; under 6 free.