I talked to Linda McDermott, the Princeton Township clerk (the Mountain Lakes House is in Princeton Township, which surrounds the smaller Princeton Borough--that's basically the downtown area of Princeton, as far as I can tell), and she sent over this document about what the deal is with getting married by the mayor of Princeton. I admired that she was very straightforward with me, though she said this information was available on their website and I couldn't find it, so I've uploaded it into my Google Docs if other people are interested in taking a look. I also thought it was rather funny that she caveated all her statements with the fact that there may be a new mayor of Princeton by the time our wedding rolls around. I couldn't quite judge what her feelings on this potential state of affairs was.
Anyway, basically, New Jersey doesn't have justices of the peace, and if you don't want to be married by a religious figure, your options in terms of government figures are the mayor of any town or municipal judges. The current mayor of Princeton evidently will do weddings on weekends, but doesn't like to book civil ceremonies more than 2 weeks in advance. These ceremonies generally just follow the standard format outline in the document she sent over and don't last more than 10 minutes. Most mayors will also only marry residents of their township, which makes sense to me but isn't particularly helpful in our situation.
The Princeton municipal court judge is Judge Goldman, who also requires that the couple be Princeton Township residents. She only performs weddings on Tuesdays or Mondays (her court day), but there isn't a fee on top of the marriage license ($28 in NJ, I think) so that's basically like a city hall/courthouse wedding.
Marriage licenses are issued by the Department of Health (609 497 7608 for Princeton Township).
So basically, what Dan and I concluded is that since we don't have any connections through family or friends to local judges or mayors, we'll probably end up going with the hiring a celebrant method instead. We'd thrown around the idea of having a friend do one of those being ordained for a day thing, but decided that we wanted someone who pretty much knows us equally well, rather than trying to do something of one friend from each side and then also be able to have someone a bit older, rather than a peer. We're in the midst of talking to a few different officiants, and I'll report back when a decision has been made on that front as well. Choosing an officiant is pretty much the last Big Decision, I think.