According to Jim Recap: Charity Begins at Hef's
Jim has never understood the obsession that Cheryl has with helping those less fortunate than themselves, but when he and Andy are helping to stuff envelopes, they come across a letter to the Playboy Foundation (and it really seems to exist), which perks him right up. Suddenly he's keen on helping, so he submits a letter in Cheryl's name, as the prize is a night at the Playboy Mansion.
You didn't read that wrong - there is a Playboy Manson in (or near) Chicago, it's just not the one regarded as the Playboy Mansion. In fact, the one in Chicago is the original - the one in LA used to be known as the Playboy Mansion West. In any case, the show didn't go into that, there were no plane trips, and a car was involved, so I'm sure that the charity event was held at the original mansion that's near Chicago.
What should be a surprise to no one is that Cheryl's name is picked to go, it should also come as no surprise that she doesn't elect to take Jim (she decides to take Dana instead), and it should definitely not be in any way surprising that Jim and Andy come up with a scheme to get inside.
At first they try to pose as members of the band, but since it's the boy's choir, they don't get in. When that fails and they find homeless people from the shelter getting in, they trade their tuxes with a couple guys from the shelter and get in without so much as a second glance.
Once there, they get to hobnob with the big guy himself (that's Hef - Jim is doing the hobnobbing) and then Cheryl is called upon to read her entry, which she really doesn't want to do, since Jim wrote it, but it turns out to be a very sweet tribute. And Jim gets his cigar from Hef.
