Drupal is what I use. In addition to the blog part, have enjoyed creating custom content types to track some interesting things in my life (cars, phones, and computers for example). Then I add a view to show them all in a table with the columns and sorting that I want for that particular content type.

In the past I have used the APIs to a very small extent. I stored license keys for an app as a content type so that they were easy to manage by employees, and the app connected to a service that called the API.

Probably any fleshed out CMS will check all but the last one of your boxes (nothing is going to be "extremely" easy to host).