eth0 as NAT is a fundamental requirement of Vagrant in its current state. But you can override the default router configuration for eth1.

From the Vagrant docs:

Default Router

Depending on your setup, you may wish to manually override the default router configuration. This is required if you need access the Vagrant box from other networks over the public network. To do so, you can use a shell provisioner script:

config.vm.network "public_network", ip: "192.168.0.17"

# default router
config.vm.provision "shell",
  run: "always",
  inline: "route add default gw 192.168.0.1"

# default router ipv6
config.vm.provision "shell",
  run: "always",
  inline: "route -A inet6 add default gw fc00::1 eth1"

# delete default gw on eth0
config.vm.provision "shell",
  run: "always",
  inline: "eval `route -n | awk '{ if ($8 ==\"eth0\" && $2 != \"0.0.0.0\") print \"route del default gw \" $2; }'`"

Note the above is fairly complex and may be guest OS specific, but we document the rough idea of how to do it because it is a common question.

The problem was that PuPHPet.com's CentOS vagrant boxes no longer come with a default set of firewall rules. So, in order to resolve this, boot up the VM using VirtualBox (or whichever hypervisor you are using), then modify and save /etc/sysconfig/ptables to allow your desired services.

In my personal opinion, the best way to edit your iptables' rules is by using a CLI tool which can easily be installed with yum: sudo yum install -y system-config-frewall-tui. This text-based user interface allows you to easily enable / disable standard services (httpd, bind, postfix, nfs, etc) using the wizard, as well as, create custom rules for non-standard ports / services (such as Webmin's port 10000). This tool is a true time saver.

If this doesn't resolve your connectivity issues, in order to rule out whether or not it is firewall related run sudo service iptables off on the guest and attempt SSH access from the host (ssh vagrant@my-host-name-or-ip).

If you have SSH access now, then the issue is going to be a FW problem and you will need to double check your iptables (did you save your changes?). If you are still unable to get SSH access, then it is most likely a networking problem and should be troubleshooted accordingly (check ifconfig, route, pinging from the host to the guest and vice versa, etc).

HTH.