To make the line around the EventBox, it is possible to put it into the Frame or another EventBox. You can try the following code:
#!/usr/bin/env python
# example eventbox.py
import pygtk
pygtk.require('2.0')
import gtk
class EventBoxExample:
    def __init__(self):
        window = gtk.Window(gtk.WINDOW_TOPLEVEL)
        window.set_title("Event Box")
        window.connect("destroy", lambda w: gtk.main_quit())
        window.set_border_width(10)
        # Create an EventBox and add it to our toplevel window
        frame = gtk.EventBox() # gtk.Frame()
        window.add(frame)
        frame.show()
        frame.set_border_width(2)
        frame.modify_bg(gtk.STATE_NORMAL,
                            frame.get_colormap().alloc_color("blue"))
        event_box = gtk.EventBox()
        frame.add(event_box)
        event_box.set_border_width(10)
        event_box.show()
        # Create a long label
        label = gtk.Label("Click here to quit, quit, quit, quit, quit")
        event_box.add(label)
        label.show()
        # Clip it short.
        label.set_size_request(110, 20)
        # And bind an action to it
        event_box.set_events(gtk.gdk.BUTTON_PRESS_MASK)
        event_box.connect("button_press_event", lambda w,e: gtk.main_quit())
        # More things you need an X window for ...
        event_box.realize()
        event_box.window.set_cursor(gtk.gdk.Cursor(gtk.gdk.HAND1))
        # Set background color to green
        event_box.modify_bg(gtk.STATE_NORMAL,
                            event_box.get_colormap().alloc_color("green"))
        window.show()
def main():
    gtk.main()
    return 0
if __name__ == "__main__":
    EventBoxExample()
    main()