Can't see Create Database in Analysis Services SQL Server Management Studio
For what it's worth, this might have to do with the mode, in which SQL Server Analysis Services is installed. If it is installed in the Tabular mode (the default), then the New Database... menu item is not available. If Multidimensional and Data Mining mode is selected during the installation, then the New Database... menu item becomes available.
A much more experienced co-worker helped me to figure this out when I was struggling with the same problem.