Comes as a bit of a shocker, doesn't it? Kenya IS an expensive place.
Much more expensive than the UK - if you asked me - and as you are going to find out.
You can try doing the Nairobi National Park on the cheap - but the experience may leave you with a bitter taste in the mouth... so the million dollar question is:
If it didn't go to your liking, would you get another opportunity (may be on this trip or on future ones) to re-visit the park?
If it is a once-in-a-lifetime opportunity, I would politely suggest you break the bank and do it "right".
The problem with Kenya is there are distinct classes of service for each category of 'clientelle'; and unfortunately Western standards, expectations, quality-of-services (or whatever else you want to call it) put most foreigners from Europe in the most expensive class of clients; and the consequent cost differential is phenomenal.
If you do want to try it on the cheap, this is how it goes:
(1) Take a "matatu" (mini bus or 9 seater micro bus) from Westlands to town. Take another one from town to Ongata Rongai and ask them to drop you off at the entrance to the national park.
I am open to correction here but I think the more common "matatus" headed to Langata turn off into a side road well before getting to the park entrance so you should avoid them.
(2) Walk the 200 - 500 meters to the actual park gates. The office block is adjacent. There is a Wildlife Service bus that departs from these gates, does a tour of the park, and brings you back. Nothing spectacular.
(3) Once you've purchased your park entry tickets from the office block (which cost an absolute fortune just because you are a foreigner) you can board the bus and join the screaming school kids (and probably other budget travellers) for the ride.
Definitely not my style.
MrGenius