Hannibal Buress would have you believe he likes to stay close to home. The 29-year-old stand-up comic has hosted a free Sunday night comedy series for the last two years at the Knitting Factory in Williamsburg, Brooklyn.

“It’s a fun show,” says Buress in his characteristically laid-back near-drawl. “Two blocks from my house. I can stumble home.” When asked to suggest a venue for an interview, he selected the Commodore–directly across the street from the Knitting Factory.

“I’m going to the Upper West Side tonight. I’m already dreading it,” he says.

His trepidation is in jest, of course. Buress, whose droll, offbeat joke-telling recalls vintage Steven Wright, is no stranger to traveling long distances to tell jokes thanks to a touring schedule that has him crisscrossing the country several times a month and traveling to London for his first-ever shows there in May. Buress will perform six shows at Caroline’s on Broadway starting tonight and running through Sunday.

After starting his stand-up career as an undergrad at Southern Illinois University in 2002, Buress established himself in Chicago. (His 2010 debut CD, “My Name is Hannibal,” was recorded there.) He relocated to New York four years ago to be part of what he calls “the best stand-up scene in the country.” It’s a scene in which he has flourished: He’s become a fixture at local clubs and theaters; he’s appeared on “Louie” and “The Late Show with David Letterman”; and Comedy at the Knitting Factory has become one of the city’s premier comedy showcases. Said Buress, “It’s packed all the time–packed when I’m gone, packed when I’m there.”

2012 is shaping up to be a pivotal year for the comedian. He returned for cameos in three episodes of the NBC show “30 Rock”–Buress was a writer on the show’s 2010-11 season–and in March he performed at the internationally broadcast Secret Policeman’s Ball at Radio City Music Hall. “That was the biggest crowd I’ve performed for. And I only had to do five minutes.”

On May 20, Buress will have his biggest night yet with the premiere of his first one-hour comedy special, “Animal Furnace,” on Comedy Central. (The uncensored special will be released on CD and DVD May 22.) Where “My Name is Hannibal” dwelled on absurd little fantasies about flicking pickle juice and kicking pigeons, “Animal Furnace” finds the comic moving toward a more expansive style. “I started telling more stories from touring, and stuff that happened when I was in Canada and Scotland.”

As for the bizarre title, Buress says it’s the result of unofficially soliciting suggestions via Twitter. “I think it’s the first comedy special that’s been named by a fan. I thought it was funny but too weird to be a title. A couple months later, the title I liked got rejected, so I said, How about we call it ‘Animal Furnace?’” (When announcing the title on Twitter, he prefaced it with, “I may regret this years from now.”)

May 20 also marks the debut of “The Eric Andre Show” on Adult Swim. Buress’ role is described as the “apathetic co-host” to comedian Andre. Adult Swim says the show takes place “on a dingy public access TV channel within an alternate reality.” Buress says, “It’s a talk show. Just a weird talk show. Some fake guests, some real guests.”

This weekend’s shows promise a mix of material from both of Buress’ recordings, but to hear his freshest material, you’ll need to catch him at an open mic night after a road gig or at his Sunday home, the Knitting Factory. “That’s where I try out a lot of new stuff. The crowd knows me there. And I can bring up the other comedians, and they can rock it, and I can be mediocre,” he said, laughing. “But I try to do well also.”