As someone on the other side of the table, I'll offer a contrary opinion. biv says he/she has not turned in a signed contract but is "definitely going" to take the previous offer. Sounds to me like there is something in writing already, so there's no reason for biv to be feeling nervous about the solidity of the offer.
Keep in mind that interviewing is nearly as stressful and time-consuming for the host department as it is the candidate. You are asking people to take at least an hour and a half (and much more for those on the search committee doing the meals and driving around) out of their busy schedules to devote to your interview—when you admit yourself that you have absolutely zero intention of even entertaining an offer.
Build your connections with the other department at conferences, but out of kindness to them, please be honest with them and cancel the interview.
If you're still ambivalent, consider this question: Imagine that somehow the committee found out that you had already accepted another offer but still came out to interview. Do you think they will approve of your actions? And then do the same exercise for the first department, where you had already accepted an offer. How do you think they would regard your actions?