Java Swing seems to place the \'Menu Text\' after the icon (if present) on MenuItems. See example below.
You could try either of these approaches:
Unicode characters are appealing, but they offer poor alignment in a variable pitch font:
JMenuBar menuBar = new JMenuBar();
JMenu windowMenu = new JMenu("Window");
windowMenu.add(new JMenuItem("♦ Item"));
windowMenu.add(new JMenuItem("✓ Item"));
windowMenu.add(new JMenuItem("• Item"));
menuBar.add(windowMenu);
frame.setJMenuBar(menuBar);
Better, implement the Icon interface, illustrated here and here, using a fixed-size implementation to control geometry. CellTest shows one approach to rendering an arbitrary unicode glyph.