Addis is a safe city you can walk around anytime of the day, taxis are helpful and not costly if you know where exactly your destination (plan ahead) the city is pretty big to get around.
One of the highlights of your trip would be to visit one of the two Yod Abyssinia cultural restaurants. This is a must see place, especially for dinner which is accompanied with multicultural dances and singing from all over the country. It's an experience you do not want to miss! Do order a "buna" ceremony (Buna = coffee). It will come with freshly popped popcorn, tiny triangular cups and an incense that you will cherish in your memories forever.
Bole International Airport is the main Addis Ababa city airport, is close to the city and main hotels in the area by the same name. Addis climate is mild almost the whole year around, except between June and September when the rainy season sets in. Addis has several main shopping buildings (malls) but they are fairly expensive compared to the local markets in the same area. You should check out the Merkato (with a guide) to get the feel of the place.