Little Ethiopia (LE), on Fairfax Blvd. between Pico Blvd. and Olympic Blvd. is the place to go for anything Ethiopian and Eritrean cultural and of course coffee (buuna). After all, Ethiopia is where the coffee bean was discovered then made it's trek to the middle east, Europe, and south, central, and north America. There are over 30,000 Ethiopians and around 20,000 Eritreans who call Los Angeles home. Eritreans and Ethiopians pretty much eat the same types of food here in the states but back in Eritrean and Ethiopia there is a wide variety of foods eaten by the 70 million Ethiopians and 4 million Eritreans.
With that being said, lets do a breakdown of the restaurants and shops in (LE) to get you feet wet and your tongue ready for the amazing tastes awaiting in LE. One can not be afraid to eat chili peppers (berbere) and you can always request mild, medium, and spicy for any dish that has berbere. Doro Wot (chicken Stew w/hard boiled eggs) is a dish that cooked by a host in Ethiopia and Eritrea if they really want to honor your presence in their home. It actually takes about six to eight hours to cook in a traditional dish. So, I'd suggest either Little Ethiopia or Awash (on Pico Blvd.) for this dish. It is incredibly tasty and the chicken meat just falls off the bones. Plus, try to beat your friends and/or family to the soaked enjera (traditional bread) towards the end of the meal...you will not regret it.
If you're looking for beef and lamb, you can also find delicious dishes at Little Ethiopia. Plus at Messob Ethiopian, they have the traditional tables, hence the name "Messob". You should also try tej (honey wine) made on the premises. Warning, it is an alcoholic drink - strong but so tasty. Thirdly, they do a traditional coffee ceremony that must be taken advantage of with at least a group of friends and family of four or more. Merkato (market in Italian) named after the largest outdoor market in all of Africa is another wonderful choice for sharing a large plate of food as are the restaurants previously mentioned. Merkato is slightly different as it has a small store attached to the restaurant. There one can find enjera, spices to make the food, tea (sha'hi), raw coffee beans (possibly to try roasting at home), and oils for eating and using for beauty regiments including henna, soap, and incense. And a few items not traditionally east African but via Jamaica.
For those of that favor vegetarian or vegan options, Rahel Ethiopian Vegan Cuisine is the place for you. Rahel's has a wider variety of vegetarian and vegan choices and a lunch buffet special that can't be beat. Food by Ghenet is slightly differentiated from the other restaurants on Fairfax Blvd. It is a bit more upscale and they tend to serve what might be called Ethio-euro-american fusion. Not really the place for a traditional Ethiopian/Eritrean meal but quite nice.
What about dessert? Eritreans and Ethiopians don't really eat sweats and only started when it was introduced by the Italians. But in LE, there is Hansen's Bakery which has been around for over six decades. Interestingly, it moved to it's present location from Boyle Heights. Hansen's Bakery has great cakes, cupcakes, etc. to take home after a meal in "LE".
So, now that you have a bit of information to help you distinguish the restaurants, go out and try some tasty door wot, tibis, enjera, buuna, sha'hi, tej, or if you're feeling a bit adventurous - kitfu.