First, yellow fever vaccination is mandatory when arriving in Kenya. Customs people (some of them can be extremely rude and looking for) rarely check but if you get the wrong guy than you ... Brought your doctor's paper saying that she can't have yellow fever vaccination. And the best thing to do, contact the Kenyan Embassy when you currently live.
4 month ?? Is she planning to give birth in Nairobi ?
It should be safe for her to come in Nairobi without vaccination as long as she stays at home, in Nairobi, and rest (don't go on safari, eat at funny places, etc.). For your information, there is no (or very little) malaria in Nairobi but mostiquo nets is recommended. Common issue for newcomers is diarrhea.
So personally, I don't see any problem as long as you play it safe => Only drink mineral water from bottles, don't ask for icecubes or fresh juices, don't eat raw vegetables or fruits without skin or anything that may be washed in running water (salad, ect). Only eat well cooked meat. Always wash your hands before and after meals. ==> well, you got it I guess.
Health facilities in Nairobi => VERY VERY GOOD, this should not be an issue.
Gyna facilities in Nairobi => There are many good gyna in Nairobi. Once you are in Nairobi, just PM me and I will give you details of one of the best.
Cost for gyna is around 30 to 35 euros per consultation
Cost for normal delivery at Nrbi Hospital is between 1 200 euros to 2 000 euros (sorry, I have no memory), all inclusive (rooms for 2 days, labour ward, gyna, pediatrician).
The only issue you may have is at delivery and after delivery.
Note that epidural is uncommon here, it can be done but I may say it is risky because they don't do it that often. After delivery, baby is immediately vaccinated for BCG, Hepatitis B and OPV and then it is non stop up to the 6-months, so if you don't like vaccines, then be prepared. I am not a doctor so I can't tell if it is good or not (please read this for vaccination schedule - )
Lastly, another thing which is not usually done in Western hospital, but note that milk bottles and milk powder are strictly forbidden in maternity ward. Breastfeeding is obligatory and nurses will do everything they can to encourage (if not force) mums to breastfeed.
I hope this helps
TheBigBoss