Switching from 120v to 208v power

You are getting the same amount of 'power' either way (120V x 60A = 240V x 30A), so from an electrical "power" standpoint it is a wash--either one will support the same amount of equipment in the rack...

You should do some research to be certain, but most modern computer equipment is equiped with switching power supplies that accommodate a wide range of voltages (manufacurers don't need to stock a separate power supply for each country; instead, they simply ship the appropriate power cord for the destination country). Given that, your equipment most likely will not care whether they have a 120V or 208V or 240V input--so long as you have the appropriate power cord to connect the system to the power distribution module.

My understanding from engineers at colocation facilities I've worked with is that most switching power supplies are a bit more efficient with a high voltage input (e.g. they produce less heat, which is wasted energy) which can save a bit on both power air conditioning load. The wire gague required to carry the same power at 240V is smaller and more flexible than the heavier wire required at 120V, which may be a convenience when routing cables within the rack.

I would confirm that all of your equipment is capable of accepting high-voltage power; if so, obtain the appropriate power distribution module and cordage to connect your equipment to the 240V 30A circuit.

Remember, too, that a 30A circuit should not be loaded up with 30A of equipment--you need to leave some "head room" to ensure that the circuit is not overloaded (I believe the rule is to stay below 80% of the maximum rated capacity (e.g. maximum 16A continuous load on a 20A circuit; no more than 24A continuous load on a 30A circuit).

As someone who worked in the hosting/datacenter management world I beg of you,

Don't Do That!

If you require 110V power contact your facility/electrician and have a proper 110V feed run to your rack - most facilities are equipped to provide conditioned UPS/Generator backed power at 110V as well as 208V, and already have equipment in place for situations like yours.
If they don't already have a 110V supply available they'll be able to work with you to provide a stable solution for your power needs.

Adding your own step-down gear introduces a number of problems, not the least of which is added load (electrical, but probably more importantly thermal) for the datacenter infrastructure, and would almost certainly be frowned upon by the DC Operations team (If it isn't you may want to seriously consider new hosting arrangements).