Weekend in Addis is complicated for me but visiting friends art studios,going for the national museum...where LUCY is and much more Ethiopian history and artifacts found (good 4 expat).Also going for the tropical garden festivals(which I don't know when but could find it's event programs on what's out Addis booklet.).visiting the "Entoto" mountain would give you full view of Addis Ababa from top....Also you can find the old Emperor Minilk Palace there.
Enjoy it.Will come up with more.
Articles to help you in your expat project in Addis Ababa