TODAY

BABY LOVES BEBOP:

He revolutionized the piano – and his name is one of the coolest monikers ever. We’re talking, natch, about Thelonious Monk, subject of Jazz at Lincoln Center’s first “Jazz for Young People” concert of the season. Expect host Wynton Marsalis (above) to have kids ages 6 and older dancing in the aisles. 1 and 3 p.m., $12, $20 and $28. Rose Theater at Frederick P. Rose Hall, Broadway at 60th Street; 212-721-6500.

HISTORY REPEATING:

There are two sides to every story – and you’ll hear both at Living History Days, when re-enactors portraying Union and Confederate soldiers talk about how the Civil War went down. 10 a.m. to 5 p.m., free with admission ($10 for adults, free for kids). New York Historical Society, 170 Central Park West at 77th Street; 212-873-3400.

IF THE SHOE FITS:

A foundering business and homeless dwarves? Gee, the kid-friendly new musical “Elves and the Shoemaker” seems the perfect fairy tale for our times. Noon and 2 p.m., Saturdays and Sundays through Jan. 4, $20. Manhattan Children’s Theatre, 52 White St., first floor, between Broadway and Church Street; 212-352-3101.

TOMORROW

ART AND ENTERTAINMENT:

From the outside, the Solomon R. Guggenheim Museum looks like some sort of fantasy playground. It comes close to being one on Fall Family Day, when little ones are invited to explore the museum and take part in art projects, storytelling and more on their own terms. 2 to 5 p.m., $15 per family (two adults and up to 4 children), cash only. 1071 Fifth Ave., at 89th Street; 212-423-3500.

STEP SAFELY:

Sprains, bruises, blisters – dancing can be as dangerous as any pro sport. Learn how to keep in top form at the ABT Healthy Dancer Open House, where advice on injury prevention, nutrition and more will be accompanied by guest appearances by Angelina Ballerina and ABT dancers. Ages 4 through 12. Noon to 4 p.m., free. 890 Broadway, Second floor, between 19th and 20th streets; 212-419-4383.