Reddit mentions of Ethiopia - Culture Smart!: The Essential Guide to Customs & Culture

If you fly in by Ethiopian Airlines you're entitled to a discount on domestic flights. not sure what that is anymore though but it is significant if you plan to do any amount of flying. It's worth it if you're going to Axum or Mekelle. Remember to confirm the return journey at the local EA office! However also what can be interesting is trying out the bus network if you're going somewhere along a main route i.e. Rift Valley lakes.

If you want to do a bit of everything I'd recommend checking either the Bale or Simien Mountains. Both packed with monkeys and wildlife as well as the elusive and endangered Ethiopian wolf. Also check out some of the lakes, be it Lake Tana or the Rift Valley lakes. Be sure to check out a lot of the religious buildings and especially the churches in Lallibella. Ethiopia has a fascinating and diverse history in this regard with influences of early Christianity, Islam and Judaism. If I could recommend a book it would be this one. It's a pocket sized wealth of information (and I wrote the sports section :P).

Most natural and cultural attractions are outside Addis but this does not mean there's nothing to do in Addis. Addis is lively and interesting. I'm sure there's another thread on this subreddit detailing the things to do.