Hey Alex! @yanokwa and I just wrapped up a month in Nairobi. We found that living a middle class kind of life cost just a little less than it did for us in Seattle, USA. You can certainly get by for less than we did but I would say that in general, food, drink and entertainment are significantly more expensive than in most of Southeast Asia.
Meals at mid-range restaurants usually set us back about $30USD-$40 for the two of us. A meal at Java House (local Starbucks coffee equivalent) for two was about $15USD-$18. I did a grocery run at vegetable stands and smaller markets and spent about $45USD for a week's worth of staples and vegetables (no meat). We did the rest of our grocery shopping at Nakumatt with meat, fish, etc and that was more like $90USD/week for two. I think Numbeo looks pretty accurate. But of course, there are lots of street vendors selling boiled eggs, grilled corn and things like that which are much cheaper!
I think you want to be thoughtful about the neighborhood you choose as rush hour lasts most of the day and getting around can be difficult. We really liked being able to walk to Nairobi Garage Westlands and generally really liked the space and people. I think it may be hard to find a room for $360USD in a convenient area. What coworking space are you thinking about?
Another thing to keep in mind is that July is the coldest month of the year. Even in May/June, we were often wearing hats, gloves, jackets and still feeling chilly! Because it's humid and overcast, I think it feels colder than it is so definitely come with the right clothing. Locals wear down jackets and boots these days.
Nairobi is an amazing, energetic city and we met so many entrepreneurial Kenyans who are doing great things. I think it's totally worth budgeting more for.