The most plain NuGet server. No database required.
Note that this is for NuGet API V3 because that is the only version with an actual specification.
Chocolatey adds support for V3 servers in 2.0.0, which is currently in alpha. You can upgrade to a preview version with choco upgrade chocolatey --pre.
Simply place your packages in the "packages" folder with the "name/version" folder scheme. If you did anything wrong, the generator script will warn you.
Then for every new package or version, you run the generator script (php gen.php). Note that you will need to specify a base, but it should be pretty self-explanatory.
The generator script produces a static "www" folder that you can deploy to any web host — they don't even need to support PHP!