It is the second attempt to plan the building after funding for an adjoining brain unit was pulled.
Initial drawings haven't changed greatly, and they will be available to see at various locations over the next few weeks. It comes as the first on-site work begins at Little France on the 130 million facility.
Brian Currie, project director, said: "We want the new hospital to be at the leading edge of clinical care for children and are working hard to ensure it is a worthy replacement for our current children's hospital – continuing 150 years of pioneering paediatric healthcare in the Lothians.
"The location of the new hospital, next to the Edinburgh Royal Infirmary at Little France, will ensure we provide the safest possible hospital care for children, with the dedicated team of clinical staff able to work closely with their colleagues in both maternity and adult services."
The designs will be unveiled at the current Sick Kids Hospital on 26 April, then moving on consecutive days to St John's Hospital in Livingston, Craigmillar Library and the Western General before finishing up at the ERI on 30 April and 4 May.