The backpackers can be easily reached with public transport from the bus / train stations in town. Nairobi's public bus system in general is quite good (and a lot cheaper than haggling with the cab drivers for a fair fare).
We stayed before and after a group of American missionaries had booked the whole place and therefore got to test two different dorms.
The dorms were clean and with enough space. Please note that there is a cheap cheap dorm in a tent which I didn't get to test but heard horrendous things about. Apart from the dorms there are also doubles.
One of the dorms I stayed at came with en suite facilities. Both the en suite and the shared bathrooms were clean and with hot water but the showers in the shared one are a bit inconvenient: there is no private space apart from the shower itself so that you have to show some artistic skills to get dressed in clean clothes without exposing yourself to fellow guests.
There is a bar / restaurant with a wide range of drinks and dishes and a cozy fireplace. Prices are ok. But if you're on a budget budget go to the eatery / market place behind the backpackers (leave backpackers, turn left, left again and up the little alleyway).
WiFi and computers with internet are available against a charge (200KSH per day). Wifi only works in the common areas and - if you're lucky - the first dorm on the left (aka the girls' dorm).
The backpackers has a travel desk where you can book all sorts of tours to popular Kenyan tourist destinations. I didn't try them but the ladies seemed to be quite capable.

Milimani Backpackers is safe, central and friendly. During the day you can easily walk into the city and the gate is always locked and guarded at night. The bar at the premises with the bonfire is cozy and frequented by patrons of all ages and nations. Great place to pick up tips on do's and don'ts. If you want to feel the local pub vibe a little closer there's an excellent sportsbar just left with only 100m to go which is safe to do on your own or with a friend.

Bedbugs are a drawback..

I only stayed in Milimani for one night, and it was okay. The food and facilities were mediocre. They said that they had wireless, but it wasn't working when I was there, so I made due with 2 ancient computers they had off to the side. The TV room was nice, but the outdoor areas were damp and dirty, so it was difficult to sit out. But, the compound felt safe and secure and the price was right.

The staff are wonderful, cheery, and so welcoming. They are knowledgeable and willing to help with things even beyond their job duties. They absolutely made staying here worth it! The facilities aren't great for the price, it'soften over-crowded and there is very little community space but you can't beat the location (just a 20 minute walk from downtown Nairobi).