What software packages are you using already? If you just want to produce maps for diagrams and figures, it's quite likely that you can find add-on libraries or packages for producing maps. For example, Matlab and R have libraries for this.
The Generic Mapping Tools software (http://gmt.soest.hawaii.edu/) makes really good maps, but it has quite a steep learning curve.
If you want tools to perform geographical analysis, again there are libraries for Matlab, R etc. around. Or you could purchase something like ArcGIS (expensive!) which is specifically designed for geographical analysis.