does it really have to be a Verizon phone? Would it not be better to buy a phone and then just use it with your network of choice? I'm in the UK, so not sure if you have that flexibility with your providers over there.
I just got the HTC One X, but it hasn't got an easy or complete bootloader unlock yet. You can root it and flash a custom ROM, but you can't update the radio without an official update yet. It's a very capable phone, but like any new device it still has bugs - in time it will be awesome, but for now it's "just" great.
The Galaxy Nexus is the modders choice, and as people have said, you can unlock the bootloader with a basic command. It has an established custom ROM community. If you don't already, I'd recommend reading the XDA developer forums for each phone you are considering.
If you consider the HTC route, be aware that the LTE One X (aka Incredible 4G) is only dual core, not the quad Tegra 3 of the GSM version.
Is 4G really a must have? For global use, a non LTE phone may be better.
Hope that's helpful!