About hospitals, I dont know much more than you do. Korle Bu and 37 Military hospital are the two big government hospitals in Accra and among those with operating theaters and specialized personnel. I have also heard about the private hospital Lister Hospital from some expats working with the UN, but have never been there myself. They have a nice website, see this link. I live in Tema and have been to the simple but nice Caiqo Hospital in Tema's community 10 when my visiting siblings fell ill. They dont have any website or contact online. I also found a complete (?) list of hospitals online, but the four I mentioned above are unfortunately all I know of personally.
Can anyone else fill in? Where do you go when you or your family members are sick?