Choosing from either a pull down menu or a simple list in CountryReports.org, you can select a country from a list of around 260. Much of the information is from the CIA World Factbook but it's a bit more user friendly. The whole site is designed for those seeking simple sets of data, so it would be useful for students of all ages, tourists, researchers, etc.
For each country you get a basic page with a (somewhat undetailed) map, national flag, the weather, some news headlines and links to other information, such as economy, defence, geography, government, history, people, national anthem and related links.
If you hit one of the links to other information you'll get a lot of the data on the one page. Each section is brief, but concise. The weather section allows you to choose from a list of cities or geographical locations for whatever country you are interested in. The national anthems are available in midi format.
Sadly, for one of the countries I looked at, almost all the news stories were from well known foreign sources, instead of national ones. Quality of coverage throughout can be a little uneven so it's always a good idea to look at several sources of information. And don't forget to check a site's sources. Too many sites depend on the same few sources for their data.