These mountains, just north of the city, are the site of Menelik’s former capital. You'll find a couple sights of interest and a great viewpoint. At the summit you're close to 3200m above sea level. On the way up you may pass by the Women Fuel Wood Carriers Project, an organisation set up to protect the rights of women gathering firewood on the mountain. Traditional clothing items, hats and baskets can be purchased. They can be difficult to find and there are no signs – the only way is to ask.
To get to Entoto, take a taxi or minibus to the terminus of Entoto Ave from Arat Kilo. From there another minibus will take you to Entoto Maryam Church. You might also be able to flag a minibus from Shiro Meda Market. If you're in Ethiopia on an organised tour and your time here involves a tour of Addis, your driver may well bring you up here – if not, ask.