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.