See my post above. The ethnological museum at Addis Ababa University is worth a visit. It is like 3-4 floors and it is in the middle of the university, so i also walked around the univ. 200 birr, foreigner price (about $4). The National Museum is skippable--not much there and poorly documented though cheap (50 birr). I took a taxi to the ethnological museum (320 birr) and walked back, about 5 miles. I stopped at a cafe mid-way back for cake and coffee. On the way back, there is the new modern public library, and I stopped in. You see a lot of Addis Ababa on that walk. I like to walk and see a city, and the traffic in Addis is not bad (I had come from Delhi, where the traffic is totally crazy). The Skylight Hotel people assumed I wanted a car and driver as they couldn't imagine that a foreigner would want to walk around. Ultimately, they called me a taxi via uber (you pay the driver in cash).
If you want to really see the major sights, you'll need a driver or multiple ubers or formal tours that exist, as it is spread out enough.