visiting Nairobi

Hello,

My partner and I arrive to Nairobi in two weeks for a 10-day trip. We would like to go on a 3-day safari. Any good (no tourist-trap) recommendations?any specific agencies to trust? which park would you recommend most?
Also, I will be doing some heavy visiting while my boyfriend is working during the week, so I'm interested in some city sights or activities I could see/do on my own. I'd appreciate any suggestion.

Thank you! looking forward to this trip :)