I agree, the CBD is much safer than it was in the 90s, or even a few years ago. And with the issue of terrorism always in the air, you can be sure there's nearly always some security guard or other standing in a shop doorway, watching out for anything dodgy. Even nightlife in the CBD has woken up in the last two or three years - lots of clubs and people on the streets, which have some decent lighting now.
You still meet locals who live and work in suburbs like Karen, haven't been into the CBD for years, and think it's a no-go zone. And you can bump into people in hotels like the Intercontinental who literally never set foot outside - just step from the lobby into a cab.
So go forth and enjoy - great views from the KICC, National Archives, Kenyatta Avenue. You'd probably take a cab to the museum, as it's jus a bit far and in a slightly more uncertain area. And do need to be very streetwise - it's not a city for dreamy strolls. And never carry around anything valuable that you don't need with you.