Westlands is a neighborhood in a big, urban city that contains single-family homes and shops. It is not the most exclusive Nairobi neighborhood, but it would be considered a nice place by African standards of wealth. The streets are narrow and often blind for drivers who would not be used to a runner.
There are few violent crimes against women but because the role of women is limited, this could be because it would be counter-culture to do much of anything alone. Most crimes are home burglaries, as you mentioned, because of the disparity between wealth and poverty.
Running, as exercise, is odd to Kenyans (even though some of the best long-distance runners come from Kenya.) A Kenyan runs as a method of trasportation--children especially are sent on long running errands in the country. In the city, many people walk along the major thoroughfares because they cannot afford other means of transportation.
The Arboretum is a very dense park of trees and plants and not often visited, but would be very limited for running long distances. Because it is empty, it might spook you to run alone.
Uhuru park is wide open but very crowded. Running there you would get some stares and have to dodge people left and right.
Is the school you are attending set on a campus? I have been to the University and a few of the Teachers Colleges. The students at these schools change into athletic clothing to play football (men) and field hockey (women) in the afternoon. If you are interested in running, I would suggest starting from your school, enlisting some of the women who would like to run with you and run around the campus.
Enjoy Kenya, a place that will change you forever!