If you don't already have an estimate of where you are pointing, the only other option I know of is WCSFixer. There also used to be the Pittsbugh WCS correction service, but it seems to be defunct now.
These tools only work with FITS files, so your first step would be converting whatever format you have into a FITS file. The FITS website has a FITS viewer page that also has a list of tools that can convert formats, although converting from FITS to something else is more commonly supported.
A note on terminology: WCS stands for "World Coordinate System", the standard used for metadata in FITS files that lets software transform between pixel coordinates and sky coordinates. If you have good WCS values, tools such as DS9 will let you find the coordinates of objects in a FITS image interactively.
If you already have an idea where you are pointing, there are more options. The simplest conceptually is to find the field were you think you are in SkyView or Google Sky and see if you can match up objects. If you can, any of the several professional data reduction toolchains have the tools that can be used to generate WCS metadata. For example, the IRAF data reduction environment has a few different options. The learning curve is steep, but not insurmountable for someone computer savvy with some time. DAOphot and FOCAS (now incorporated into IRAF?) are other options.
If you already have an approximate WCS solution, there are several other tools that will help refine the solution. The astromatic.net toolchain is one example. (I believe astrometry.net uses astromatic.net software "under the sheets," while WCSFixer uses IRAF.)
The algorithms that can determine pointing without an initial guess generally use triangles of stars in the field, because the angles in a triangle are the unchanged by rotation and scale. However, these algorithms can work poorly in highly distorted images. See Campusano et al. 1994 and Tabur 2007 for more details.
Another tool of interest is DS9's catalog overlay feature, but its more useful for confirming that your WCS is correct than it is at doing something about it if you find that it isn't.