On Monday night, NBC's storied Tonight Show kicked off a new chapter in its old home city, New York, with its new host, Jimmy Fallon. As Fallon noted in his introduction (watch above), he follows Steve Allen, Jack Paar, Johnny Carson, Jay Leno, and — famously briefly — Conan O'Brien. Fallon made a few lighthearted jabs at the Leno-Conan debacle, and he promised to make fun of everybody — "anyone I can make fun of, I will," he said — but mostly he kept things nice.

From the moment he stepped onstage, "Fallon struck a sincere 'aw shucks' tone," says Meredith Blake at the Los Angeles Times. "Gratitude and humility are admirable traits," says USA Today's Robert Bianco, but "there were times in Monday's opening moments when Fallon risked taking them to uncomfortable extremes. One more 'thank you,' one more 'I never thought I'd be here,' and viewers might have wondered whether they wanted to be there themselves."

That last bit may be a little unkind — earnestly good-natured is kind of Fallon's thing — but it gets to the heart of Fallon's challenge at The Tonight Show. Alessandra Stanley at The New York Times — who starts her review of Fallon's debut with "What a nice young man" — says NBC will have to find a way to bridge the gap not between Fallon's younger audience and the "baby boomers who were loyal to Jay Leno" but between "Tonight vs. tomorrow." Stanley explains:

The Tonight show is in good hands, but its longevity rests less on the host than on audiences who increasingly don't turn on a television to watch television.... [A kid today] can watch Tonight on his iPhone on the school bus the next day.... Paradoxically, a format that hasn't changed since Mr. Carson codified it (monologue, celebrity, musical guest), is ideally constituted for the cut-and-paste ethos of YouTube and Twitter. Far more than a drama or a reality show, a joke or musical number can be plucked and posted online as a stand-alone. There is no need to DVR anymore: Why record the cow when the internet and social media can give viewers the milk for free? [New York Times]

Fallon's Late Night got that, actively courting the "viral video" effect. And he seems to have carried some of that over to The Tonight Show, bringing on Will Smith to reprise Fallon's "Evolution of Hip Hop Dancing" routine:

Along with Will Smith, Fallon had on U2, who performed one song atop Rockefeller Center and another from the studio.

But the most talked-about moment of Monday night's show was probably the parade of famous people who walked on to throw $100 bills on Fallon's desk:

The joke is that everyone from Rudolph Giuliani to Seth Rogen had bet Fallon they'd host The Tonight Show before he would. Oddly, the only person who actually might have sat in Fallon's chair, occasional Carson-era stand-in host Joan Rivers, was sandwiched in between Tracy Morgan and Kim Kardashian.

Still, nothing in Fallon's Tonight Show debut was better than his smart farewell from Late Night, with Fallon, channeling Levon Helm, performing "The Weight" with the Muppets. The unexpected Last Waltz reference, singing pigs and frogs and Gonzos, and the implied graduation from childhood to the adulthood of the Tonight Show — it's as good a way of ending a show as I've ever seen. And that may be the most promising sign for Fallon's Tonight. Watch: