I am making a 2D Java game with Java's own drawing library. I was wondering how I would make a tile map display on the screen. I would prefer to use a GUI application to make the maps. I'm looking for orthogonal projection: a top down view.
You can try using Tiled Map Editor. This editor has GUI for you to import tiles, make maps and outputs in XML format. You will need to parse the XML data in your game according to your needs. The XML format is described here and you can refer to this page for java XML parsers. There is a lot of sample games made with Tiled and documentation here.