Most important detail is missing: do you have a network connection between old and new site ?
Yes we should have a wan connection between the two.
vMotion Migration would be what I would use, if you have the licence for it. It will allow you to move your VMs while powered on. You will need to make sure the all the networks are pre-created at the other site for it to work. Which will also allow you to keep all of the VM IP addresses the same.
If you dont have vMotion then you can do a move from one data store to another data store while the VM is off. Then powering it back on when its been moved over, you should also still be able to keep the IP of the machine the same, provided that you don't power on the original one as you will have a conflict of IPs.
Thank you for the reply,
Would this be vmotioning over a stretch cluster as in the VMware Vsphere Metro Storage Cluster?
You could, but if it was myself doing it, I would have separate data stores, so I wouldn't stretch over the cluster.
When doing a migration like this, I find the key thing is to try and keep things as simple and separate as possible so, that once everything is working at the new site, cleaning up the old site is as simple as possible. Nothing worse then making something so over complex that when you turn the old site off things brake and your on the back-foot having to work out how to get things back.
Also by having separate data-stores you know 100% that host is now running on the new data-store and not running over the link between each site. Which means you can be safe in the knowledge when you turn the old site ESXi host off things aren't going to break.
If you don't have the option of deploying a new vCenter Server/Appliance don't worry, you can still do everything under one vCenter. But the below image should give you an idea of what I am talking about.