Have a look at the Hubble Deep Field image.

I downloaded the 1024x1024 version of this and the Photoshop histogram reports that about 95% of the image is dark. From this (somewhat cavalier) measurement I deduce that about 5% of the sky is blocked out by galaxies up to 13 billion years old. I'm not sure what difference going back even further in time would make, though presumably if you go back far enough the surface of last scattering would block out 100% of the field.

Note that the deep field deliberately chose a direction in which there were few stars, however only the bigger closer stars show a visible disk through Hubble, so I'd guess that the stars make little difference. Dust clouds will make far more of a difference, but you've already accounted for that by taking the Milky Way into account.

Response to comment:

How about the picture in http://www.eso.org/public/images/eso1243c/ (there's nothing special about this - I just Googled for "wide field view of sky")? The Adobe histogram trick reports around 95% of the image is dark, though the cutoff isn't that sharp so it could be as little as 90%.

This image won't show faint galaxies, but on the other hand the limited resolution makes the stars look bigger than they should be (i.e. they cover more pixels). I'm not sure how you'd come up with a definitive answer since it depends on the resolution and sensitivity of your telescope. Still, I'd guess somewhere around 5% is not a bad estimate.

Later still:

Actually this is quite interesting in a Friday afternoon sort of way. Consider this:

The Milky way contains 100 billion stars and is about 100,000 light years across. The Sun is about 8.3 light minutes away. Suppose the average star is the same size as the Sun (probably an overestimate), and the average distance from the Sun to other stars is 25,000 light years (the distance to the centre of the galaxy), then the average star appears about 1.5 billion times smaller then the Sun. So altogether the 100 billion stars cover about 65 times as much sky as the Sun covers. The Sun subtends about half a degree, which is about 0.0005% of the sky, so all the stars in the Milky way cover about 0.03% of the sky. That backs up my claim that the area covered by the stars can be ignored.

How much of the universe is observable at visible wavelengths?
Which casing looks better to you for a jQuery plugin:

$("#foo").runMyPlugin();


or

$("#foo").runmyplugin();


Is there a naming convention for jQuery that prefers on over the other?

Thanks in advance!
