From the top right (hamburger) menu icon > Sites. You can select multiple sites to publish, however you cannot select which destinations to publish to, it will publish to all enabled and checked by default destinations. If you need to select the destinations, you can right click on the site name and select Publish. Then you will get a destination selection window.
If you are in a site, you can publish it from Manage Site > More > Publish.
If you are in a site in the Site Content area, you can publish the top level folder, either from the right click menu or navigate to the folder and use the publish button near the top right.
