I need this every now and then, and I'll always run into the Microsoft website's bad installation experience, which doesn't seem to work with chrome or Firefox - no, you need IE.
There is a web platform installer making this easier, but that unfortunately doesn't install the v2.3 Azure SDK.
I took those links from this MS site.
So here they are, and a little hint for me what I need for VS2013 and compiling Apps into Azure Roles:
WebToolsExtensionsVS.msi
WebToolsExtensionsVS2013.msi
WebToolsExtensionsVWD.msi
WebToolsExtensionsVWD2013.msi
WindowsAzureTools.vs110.exe
WindowsAzureTools.vs120.exe - my pick
WebToolsExtensionsVWD2013.msi
WindowsAzureStorageEmulator.msi - my pick
WindowsAzureLibsForNet-x64.msi - my pick
WindowsAzureLibsForNet-x86.msi
WindowsAzureEmulator-x64.exe - my pick
WindowsAzureEmulator-x86.exe
WindowsAzureAuthoringTools-x64.msi - my pick
WindowsAzureAuthoringTools-x86.msi