There is so much information on the internet that it can be intimidating to try and figure out what information to trust. I will list some websites that consistently are good, reliable resources of information.
The American Academy of Pediatrics, the major national organization of pediatricians, has a wonderful website called Healthy Children. It is a wonderful resource for many topics. I would rate it the top, reliable website for information on children's health.
Another helpful website is Kids Health. It is run by a large nonprofit organization: Nemours. They cover many topics and has excellent information.
If you are looking for information about a specific illness or about specific information about health risks in a specific country, the Centers for Disease Control and Prevention website is very helpful. Their information is top notch.
One of top children's hospital in North America is Toronto's The Hospital for Sick Children. Their website at this link is comprehensive and helpful.
Our local hospital, Nationwide Children's Hospital, has a very nice website that has some good information.
I hope these are helpful!