Lots of folks are using the Garmin BaseCamp software (because it's free, it interoperates with the handheld Garmin GPS units that everyone uses, it ingests KML files, etc.)
ArcInfo (from ESRI) is a defacto standard in the GIS world (much like AutoCad in drafting for small shops). There's also MapInfo (part of Pitney Bowes, now, I think).
Note that Google Maps *can* be run without internet connectionshttp://www.google.com/enterprise/earthmaps/deployment_options.htm
The real issue isn't so much the software, but the ongoing aspect of keeping your databases up to date, rolling updates out to the portable units, etc. Especially so with respect to integration with locally generated data (e.g. things like fire hydrant locations).
If you are willing to be tied to APRS, there's a variety of software out there, but the APRS world and the rest of the GIS world are fairly distinct and separate. They address very different needs and user populations. I don't know that I would advocate APRS in a system that is going to interoperate with a local agency.
Bear in mind that GIS usage and technology is going to be continuously improving and changing. WHatever you do should allow for changes in the visualization and user software and for new forms of data ingest, while keeping your substantial investment in databases usable. Make sure that data formats aren't too proprietary, and have some longevity beyond the tool of the day.