Try Stravinsky's Firebird Suite. Also his Rite of Spring - did you know it caused a riot about a century ago? Worth looking up.

Also, anything by Sun Ra. Eric Dolphy, too. Try "Out to Lunch." Captain Beefheart's "Trout Mask Replica" is a classic, but my sentimental favorite of his is "Lick My Decals Off, Baby." Get familiar with the Residents. Their "Commercial Album" is fairly accessible and a good introduction.
Not quite as far out is Ali Farka Toure. His fusion of Delta blues and Malinese music is familiar and exotic at the same time. A great intro to world music.
Also accessible is Olivia Tremor Control's "Dusk at Cubist Castle." You'll hear their psychedelic roots from the Beatles and Beach Boys before it descends into art noise and experimentation, only to come back darker and stronger. Likewise, their "Black Foliage," which isn't as accessible. You need "Cubist Castle" to unlock it before you can explore how it treads the line between music and noise.
Speaking of the intersection between music and noise, Wilco's "Yankee Hotel Foxtrot" does the same. It has a lot of mainstream appeal, but you'll absolutely find experimentation.