etiquette - Should I let potential employers know I have a job offer?

I've interviewed for a few positions, one of which has made me an offer. I'm very pleased with the offer, but I prefer some of the other positions. I have the luxury of being able to take a lot of time to decide whether or not I accept this offer, so I'm certain I will hear back (either positively or negatively) from the other positions before a decision is required for the offer I've received.

I'm trying to decide between two courses of action, and I want to choose the one that will best help my candidacy with the positions I've yet to hear from. Plan 1 is to do nothing and simply wait to hear back from the other positions for which I've already interviewed. Plan 2 is to be in touch with the other positions to let them know I have an offer, and ask where I stand with them.

Would Plan 2 make me a more desirable candidate with the other positions, as they might see my offer as further validation of my credentials? Or, might initiating with the interviewers in this way be detrimental to my candidacy, perhaps making me seem pushy or self-centered? If so, I would rather just wait for them to run their course of action (Plan 1). As I've said, I have plenty of time, so I don't want impatience to hurt me.

If there is a good chance that my meddling will be detrimental, then I'd rather be hands-off here. However, if it's more likely that informing the other interviewers of my offer will give me a boost, then I'd want to do so.

Thanks for any clarity you can provide!

Edit: For a bit more information and context, the position I've been offered is a non-academic research position that my advisor has described as "prestigious." The other positions for which I've interviewed (and which I prefer) are mostly academic teaching-centered positions (visiting assistant professors, tenure-track at smaller four year institutions).