@Alfa
From my experience,i would go with Mater anytime! Your wifes' buddy might have met the wrong nurse or had too much expectations...was it her first kid? But,generally.Mater is the best. You can follow up with the post natal package and the fantastic 'well baby clinic'. As for their rates,am not sure how much it is this days....so just call them and ask or passby and pick their brochures+rate card.
Second option,Marie stopes. This is their major field(reproductive health),and they handle it very well. Their rates are very friendly and they have branches covering most parts of the country.
Despite not personally knowing anyone with experience from Nairobi Womens and Coptic hospital,I hear they are equally good. so it's worth a try too.
The whole birth process is mostly psychological,so involve your wife in the decision making,and as someone said here before,dont be fooled that the more expensive the better it is....even the cheap ones deliver healthy,bright babies too! Let her be prepared,physically and psychologically....and all will be well. All the best

Advice is what we ask for when we already know the answer but wish we didn't..
Nevermind what haters say, ignore them til they fade away - Just live your life