Doing Math Research in a "non-mathematical" environment
The proximity of a large university can be a big plus.  Here are some things you might find helpful:


Get in touch with the people in your field there, telling them you are in the area and are interested in keeping up with mathematical activities in their department.  Ask to be added to their mailing list for seminar announcements, etc.
Try to arrange your teaching schedule so as to be able to attend seminars at the big university at least occasionally; regularly, if possible.  If there is dinner after the seminar, try to go.  Talk with the faculty (and the visiting speaker) and look for shared interests, that might lead to things you could collaborate on.
See what kind of access you can get to their library.  At minimum, you should be able to walk into their library and use MathSciNet, read books, download papers from their journal subscriptions, etc.  You can probably also arrange borrowing privileges, and possibly remote access, either as a member of the general public (maybe for a fee) or as a professional courtesy based on your affiliation with your own institution.  The university's faculty in your area might be able to help if you run into bureaucratic hurdles with this.  


Also, don't discount your own institution's library.  Even if they don't have much in the way of books and subscriptions, it is very likely that you can get almost anything you want via inter-library loan, albeit with some delay.  Get to know your professional librarians.

And a note regarding funding: it's not unusual for conferences to have some travel funding available for participants.  (This is more common for smaller specialized conferences than for big general events like the Joint Math Meetings.)  Fresh PhDs like you usually get first priority for this, so try to take advantage while you can.