http://olololodge.com/ is on private land bordering Nairobi National Park. They just joined the marketing group New African Territories. I totally agree with the above advice to visit Nairobi National Park if you are looking for big five on a budget. Ololo would be the perfect place to base yourself from. After staying here for 1 night you can fly to the Mara and visit Spekes Camp. They have not announced their 2016 specials yet but I would be surprised if they did not have stay4-pay3 or stay4-fly free for next Feb.
http://www.africanterritories.co.ke/...ekes-camp.aspx
I have sent their reps an email to see what specials they have and, time permitting, I will re-post here soon. I suspect this 6 day program (Spekes x 4 and Ololo x 2) will be in your budget range.
Craig Beal - owner - Travel Beyond