The Pyramids of Giza are within easy access if you stay in Cairo, approximately 8 miles from the Giza site.  Youth hostels abound in Cairo and you should find other backpackers at the May Fair Hotel, at 9 Aziz Osman st, Zamalek, Cairo.

From the hotel:

"May Fair is located in the exclusive Zamalek area, near downtown Cairo. We are within a 5 minute drive of Midan Tahrir, but escape the noise of the big city because Zamalek is an island in the Nile. Our hotel is in a very quiet and safe area of Cairo, surrounded by many foreign embassies and international banks. The busy shopping area on Sharia 26th of July is only a 2 minute walk away. Breakfast and drinks are served on our big sunny terrace where you can plan your adventures in Cairo, meet fellow travellers, or simply relax. We offer you the free use of our kitchen if you wish to prepare your own meals. Our friendly and helpful staff will make you feel at home during your stay in Egypt. We can pick you up or drop you off at the airport. If you wish, we can provide you with information about tours in Egypt, and can assist in arranging these for you."