I have previously written about how you via REST can retrieve the Search Center URL for a particular SharePoint site.
If you are already on a page which has a search web part on it, you can get the same value from the page itself with the following command:
Srch.ScriptApplicationManager.get_current().states['searchCenterUrl']
To be clear; when a search web part exist on the page search Search.ClientControls.js is loaded and makes the Srch namespace available.
