The first is King Faisal hospital, but it is a little bit expensive (on a local context). It is located in Kacyiru near the Umubano hotel. If you don't have issues with money, i would recommend you this one. The second which is affordable is La croix du Sud hospital which is located in Kisimenti, Remera, near hotel Chez Lando.
Hey, had my first baby here. Went to la Croix through out, saw Dr Nyaringwaya[sp]Didnt have any complications and it was a pleasant experience all things considered. oh and their rooms are pretty decent.