I live in Nairobi and I also do not think it's worth spending four days here. Would advise you to spend two days and use the two others to go to some nice place such as Lake Nakuru reserve (pink flamigons and rhinos), Lake Navaisha (hippos and a lot of green) or even Amboseli (elephants at the foot of the Kilimandjaro).
As for Nairobi, the best place to chill out is the leafy neighborhood of Karen where white Kenyans live. You can visit Karen Blixen house, the David Sheldrick foundation (babies elephants), the Giraffe center (feeding center) and spend some nice time chilling out in the garden of of famous Talisman restaurant, which is my favourite, or Rusty Nail.
In Nairobi itself, few people live in dowtown, which has close to zero interest, except for some good dancing spots. The expat nightlife is mainly in Westlands and Hurlingham, with bars such as Gypsy or Mercury in Westlands, and nightclub Casablanca in Hurlingham next to a very good Italian restaurant, Osteria del Chianti.
Carnivore does not have any interest, apart from being crowded with tourist groups. If you really want to go there, it's better to sit in the bar, the Simba saloon, which has the same meals but offers African music amid Kenyan clients.