There are some particular API's in Java that make it very good. However I would prefer C++ because of performance and "bleeding" edge support with OpenGL and OpenAL among the many libraries.
Which API's are there that are similar to Java2D (I know I can use OpenGL however I lack the matrix math understanding to fully use OpenGL in this way)? Also which GUI framework (non-native; platform independent) is the most used in C++?
If you want platform independent GUI framework for C++ check Qt.
I can't speak much for Java2D equivalents but as far as GUI frameworks go, I've heard of two:
wxWidgets: http://www.wxwidgets.org/
Qt: http://qt.nokia.com/products/
Both of these are cross-platform and I believe widely used.
FLTK, Fast Light Tool Kit has some 2d functionality. It's somewhat like swing and 2d mixed together. It does focus more on the UI aspect but it may help you out.
Try GTK--. It has some features that make it a bit nicer an API than either wx or Qt.