Agree the Gayer-Anderson museum is worth it.. a very personal collection of artefacts in a fascinating building.. it's listed in the Lonely Planet.

For a one day outing, it's possible, if you get up really early, head to the pyramids for a quick view (from the street by the KFC for Sphinx, and then from near MENA House Oberoi for a second breakfast) and then don't bother walking around them or going in.. you could then head back to the Gayer-Anderson Museum, then down to Coptic Cairo, which is also worth wandering around.

I'd leave the Egyptian Museum.. the Tutenkhamun death mask is on tour outside the country at the moment I believe, and eventually the whole kit is moving to a new site.. wait until that is open in about 10 years.

Visa.. just bring $15 cash and buy the stamps in the hall before passport control, stick them into your passport yourself, fill in the form and hand it all to the passport control official in the booth. easy.