If you use the Team Foundation Service (on visualstudio.com) as your source control system, you can build your sources in the cloud, but access the build outputs locally.
Just start a new project on visualstudio.com and add a solution with some projects to it.
In my case a ASP .NET Web Api 2.0 project, a integration test project and a unit test project:
In the source control explorer it look like:
Create a build definition
Create a build definition in Microsoft Visual Studio 2013
If you choose for the option "Copy build output to the following Source Control folder (this folder will be created if it does not exist)".
The output of the build will be put in TFS.
So after the build you can download it from TFS and deploy locally.
Downloading can be automated by using PowerShell or some other tooling.
When you choose to put the output of the builds in TFS, you will find a "Drops" folder in the source control explorer.
The build result summary, shows some statistics on the build:
The builds can also be executed online and the result can also be seen online in the browser: