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? I find myself in an unfortunate two-body problem situation. My fiancée got two offers earlier this year, one a post doc and the other a tenure track position. She deferred the tenure track for a year and is currently halfway through her post doc. The university she got the tenure track position from was happy to do this for her so she could broaden her teaching and research skills.

I am a PhD student who is finishing up in May, but I find myself not having many good options for employment. The area in which she got the tenure track position is very small and there are not many options for people with a math PhD outside of working for one of the universities. Obviously I knew this already. However, none of them are hiring for this coming year.

The two body problem in academia is a classic problem and it's not one that is easily remedied. I'd really hate to be a lecturer because that's a really rough lifestyle and I have a lot of research I want to do. I have at least three or four papers lined up for the next year or so in addition to one I have published, two that I have submitted, and another I'm submitting in the next week or two. I'm starting to feel a lot of dread about this. What should I do (or even my fiancée do) to get an academic position for the fall (ideally in the area she will be in)?
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.