My husband and I were in Nairobi from Dec 12th - Dec 16th and stayed with relatives. It was my husband's second time to Africa and my first.
On our first day we went to the Elephant Orphanage and Giraffe Orphanage (both off Langatta Rd). You have to be at the Elephant Orphanage before 10 as they are only out for about one hour. We didn't get a chance to interact with the animals so I wouldn't really recommend going unless you love animals and aren't going on a safari. The Giraffe Orphanage was awesome as we got to feed the giraffe's and pet them and got some awesome pictures and videos.
We spent some time at Diamond Plaza which I loved - they have great food, good service and some shopping. There are a few internet cafes there too which we used. You could easily spend 4+ hours here.
We went to Carnivore and Hashmi's - I wasn't too impressed with either. Carnivore doesn't serve game meat anymore and we got sick after eating at Hashmi's, but the food was pretty good. Stavrose was excellent and I'd recommend going there.
We did a lot of driving around as it isn't always safe to walk around. I found the traffic to be crazy, crazy, crazy! So allocate extra time for that.
We also went to the animal orphanage (Kenya Wildlife Services) and played with the animals - its best to go in the morning because they aren't as hot and aren't tired from just having been fed. We spent about 1-2 hours here but I think you can spend more. I would recommend getting a guide (we found one waiting inside at the front gates after we paid) - they get you in and share some stories with you - they don't charge but just give them a nice tip at the end! I believe its $10USD for non-residents to enter.
We went to the Masai Market which is only open on Friday's. I highly recommend going here - we did most of our shopping here and it was also fun to see what the locals make and sell. Always bargain (to less than half the price they tell you!).
We visited Westgate Mall and did some shopping there - its a completely modern shopping centre (with AC)! And we liked going to Nakumatt (grocery store) to stock up on snacks, drinks and fruits.
Overall, don't flash your camera or wallet. We didn't wear any jewellery on this trip at all and didn't go out too late at night. I found it at times difficult to get fresh air because of the burning garbage, and heavy traffic. And of course the poverty and racial treatment was a shock for me. It was a very interesting experience and I had a good time. We then travelled to Arusha by plane to start our safari!
If you have any questions feel free to ask.