It's possible to go to Ethiopia practically any time of the year : in fact, temperatures are always pleasant, at around 20 degrees. If you're allergic to the heat, avoid the summer months in the east and west of the country. Generally avoid summer, as the rain can be heavy throughout the country. Please note also that in the South, the rainy season stretches from April to September. Apart from that, you'll enjoy sunny and warm weather in Ethiopia whenever you choose to visit the country.
Ethiopia has long been suggested to me as an interesting off-the-beaten-track destination. Being more interested in culture, I did the northern heritage circuit, two weeks solo trip with driver. The highlights were, as expected, the Timket festival in Gonder, the unearthly landscapes of the Danakil Depression, and the rock-hewn churches of Lalibela. Skip the Blue Nile Falls (trickle, really), and fly to and from Lalibela because the road is long and ghastly.
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RAHB
4
Lake Tana monastery, Gondar, Simien Mountains, Lalibela churches, Lake Chamo hippos, Dorze tribe, and Maze national park camping.
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Margui
5
I loved Ethiopia. It's a very varied destination. Tourism isn't developed which I liked. The Bale mountains were spectacular, and the lakes and hot springs quite incredible.