Fiancée has a position lined up, but none of the universities in the area are hiring. What else can I do to get an academic position in the area?

You (or rather, your fiancee) should talk to the department where she will be taking the tenure-track position. Many universities try to support the employment of faculty members' spouses/partners, as part of their family friendly policies. This support can take a number of forms.

The simplest form that the support can take is for the university to hire you in an academic position. You don't mention whether your fiancee is also in mathematics, which may be relevant. It's often easier to get the school to hire a partner in the same department. The reason is that the hiring has to be done with the approval of the department that is going to be employing the spouse, and that may be easier to get if the department has already made a commitment to one member of the couple. Sometimes (and ideally, I would say), the trailing spouse can be hired in another tenure-track positions.

Other times, the trailing spouse may be hired in a non-tenure track position, but one which can nonetheless be effectively permanent. You say you do not want to work as a teaching-oriented lecturer. Unfortunately, you are unlikely to get a permanent, non-tenure-track position in math as anything else; academic positions in math almost invariably involve teaching. The situation can be somewhat different in the laboratory sciences, where people can be hired as research scientists with little or no teaching component to their duties. At my institution, I know of a case where a professor was hired in the physics department, then his partner was hired as a research professor in biology.

The third possibility is that, even if they cannot offer you a suitable academic position, your fiancee's university may be able to help you locate some other kind of employment. Some schools have official policies that offer this kind of support; but some do not. However, even if there is no official policy supporting this, you may still find people (especially in your fiancee's department) willing to assist you. The help could come through personal connections, or making some of the resources of the university's career office available to you. After she finished graduate school, my own wife got some help from my institution finding job leads, which were extremely helpful.

There's nothing particularly unusual about your situation, but I'm a bit confused by your post. What have you done to try to obtain employment thus far? It would pretty late to be just applying to TT or postdoc jobs now. Have you applied for positions in other cities? As other people have mentioned, the lack of any discussion of whether you tried to negotiate a job for you when your fiancée was offered her job (and what happened if you did) seems like a pretty big oversight. I'm going to assume you have asked and were turned down (since if you haven't, why are you talking to us and not her chair?).

Unfortunately, you face some nasty choices here. My personal recommendation is to try to get a job somewhere else. Being separated from your partner sucks, but your other options are probably being a lecturer or being unemployed, both of which will be bad for your long-term prospects.

In the long term, you should expect that you and your fiancée will have to apply for TT jobs elsewhere (either to actually take the jobs, or use as negotiating leverage). So, what you should focus on is being marketable when you do that in a year or two. So, get the best job for your career in the long-term wherever that is, and get used to flying.

If you really can't stand to be apart, you can contact local universities, even if they aren't hiring. It will be bureaucratically impossible to make you a TT offer at this point (it's way too late this year for that), but they may have lecturer-type positions for you. Often in the spring, they'll realize that they have teaching needs (someone decides to take a job elsewhere or take a leave, and they end up with a hole in their teaching schedule). But since you've said that's not what you want, that just circles us back to the long-distance option.

This is essentially an impossible question to answer, but I'll point out a few things that might be useful. (I'm a physics professor at an R1 university in the U.S.; parts of this may or may not be relevant to your field or area.)

The very best thing you can do to get a long-term academic position in the same geographic area as your fiancée is to be the best you can possibly be in your field. This may sound like a silly thing to point out, but I think it's under-appreciated. Creating positions, or even creatively making use of existing positions, is tough; a really good motivation for faculty to work on this is for them to really believe that you would be great to have as a colleague. Conversely, if they are not very excited by you, doors will not open. I've seen this happen many times. (And, it makes sense.) You might not like this, but if staying away from your fiancée for a year and working on your research at some other position makes you a stronger mathematician, it will probably help both of you in the long run.

Another route is for your fiancée to threaten to leave unless a position is found for you. Given that she hasn't actually started, though, this would be a bad idea -- it will generate a lot of ill will, which junior faculty should try to avoid. Of course, and I know this doesn't help you, the time to have negotiated and set this up would have been before she accepted the position, when it would have been very normal and understandable.

A third path is for you to take some sort of adjunct-like position, assuming such a thing exists or could be created. In my experience, people over-estimate the likelihood that this will morph into something "real." (See item 1.) I should also note that creating a job for a particular person is often difficult or sometimes even illegal (in contrast to running an open search.)

Good luck!