IN TOWN There'll be a free walking tour of Mount Pleasant Saturday from 10:30 to noon; meet at the Mount Pleasant Public Library at 16th and Lamont streets NW; 234-1141 . . . The Kennedy Center Friedheim Awards competition finals, for the best new instrumental chamber music work by an American, are Sunday at 3 at the Kennedy Center Terrace Theater. General admission tickets are free, and available in the Center's Hall of States at the Friends volunteer desk; 254-3600.

IN MARYLAND The Washington International Horse Show continues through Sunday, with a concert by Lynn Anderson Saturday evening after the day's events, and jumper and hunter competitions through the weekend; $10, $15 and $25 each evening, $3 and $5 during the day; 432-0200 . . . Montpelier Cultural Arts Center at 12826 Laurel-Bowie Road holds its sixth anniversary celebration from noon to 5 Sunday, with artistic demonstrations through the day and a bluegrass concert from 2 to 4 in the Main Gallery; 301/953- 1993; free.

IN VIRGINIA The D.C. Open Chess Championship is at the Westpark Hotel at the Key Bridge in Rosslyn. Rounds are 10, 2:30 and 7 Saturday and 10 and 3:30 Sunday; registration is 8 to 9:30 Saturday ($30-$40); admission for spectators is free; call 620-9489 between 9 and 5 Friday.