Java bindings for Cairo are available in the java-gnome user interface library, with just the sort of API you'd expect:
surface = new ImageSurface(Format.ARGB32, 200, 200);
cr = new Context(surface)
cr.setSource(0.0, 0.0, 0.0);
cr.moveTo(25.0, 25.0);
cr.lineTo(50.0, 100.0);
cr.stroke();
you can use the Cairo coverage in java-gnome for drawing custom widgets in GTK, outputting PDFs, and of course images in bitmap PNG and vector SVG form. The Pango library is used for drawing text.
java-gnome is packaged in Debian and Ubuntu (there's also a PPA with the latest release) as the libjava-gnome-java package, and in Gentoo as the dev-java/java-gnome package, and in many other fine Linux distros. Check your TV Guide for details.
JavaDoc API documentation is in the doc/api/ tree and available online as well. The Context class in org.freedesktop.cairo is a good place to start.
There is example code in the doc/examples/ tree.
If you want to build java-gnome yourself there's a README to get you going. You can browse the source code online or get the code from Bazaar; you'd be best off following the HACKING instructions if you'd like to checkout the code. Releases are at ftp.gnome.org.
Questions can be asked in the #java-gnome IRC channel on irc.gimp.net, or by mailing the java-gnome-developer mailing list.