Is it appropriate to ask for a $220k piece of equipment on an ESI R01 application to the NIH?
Get the tool that helps you do the job properly and efficiently.  Your previous experience and history of using another instrument makes your case stronger, not weaker.  Shows you will use the machine.  It's not some new angle, for you, that might get abandoned.  
I really doubt NIH gets into the minutia of where competing machines are located.  If you get any static from the school or NIH, just put on a confident face and say "I need it...it's a workhorse machine for my lab."  Don't be bashful.  Fortune favors the bold.
The one thing is I would think about if you will be able to maintain it properly.  E.g. if you're a synthesist, probably not best to buy an SEM.  You almost need a technician or a group of SEM only types to keep it aligned and the like. But if you think you can handle running it and keeping it going, go for it.  Maybe mentally budget some ongoing costs for techassists from the vendor.  So if you are going to struggle with it, or it will be a waste since you have a hard time keeping it operating, then pass and use the remote facility instead.