Error VT-x not available for Vagrant machine inside Virtualbox

You can only use one virtual CPU without VT-x. Thus, the error message stating that VT-x isn't enabled is caused by the following line:

vb.customize ["modifyvm", :id, "--cpus", "2"]

Replacing it with the following works (Vagrant has a shorthand for setting the CPU count):

vb.cpus = 1

NOTE: You can only run 32-bit VMs inside another VM.

UPDATED: As pointed out below, you can use nested VirtualBox + vagrant provided that only 1 virtual CPU is assigned to the nested VM, plus nested VM guest is 32-bit OS.

Vagrant in nested Virtual Box

First of all you can run definitely Vagrant inside a nested Virtual Box.

VT-X Support (related to VirtualBox)

Currently VirtualBox is not supporting nesting VT-X. There is currently a feature request pending(see.: https://www.virtualbox.org/ticket/4032) but as of now it is not expected to be in a new version of VirtualBox

Consequences from missing VT-X in nested VirtualBox

There are currently two consequences from nesting without VT-X:

1. You cannot use multiple CPUs but you can use a single virtual cpu using vb.cpus = 1
2. You cannot run a 64-Bit VM within a nested VirtualBox.