Hi I'm starting work on a mod that would import institute armor (and possibly some amazing institute mod armours) into the world of FNV. I want to try to bring them into the world in a natural way; if not at the very least a chest with a letter explaining why the stuffs there.
I'm having trouble thinking of a reason that institute stuff would be all the way out west;
any suggestions?

I think the simplest explanation is the same they used on the Fallout 3 quest, a synth escaped with the help of the Railroad to the Mojave and they sent people to get him back.

One of the CIT's most famous pre war alumni was Mr House. It is possible that the institute may have sent synths to the Mojave to investigate the possibility that he was still alive after a mysterious "Mr House" surfaced in New Vegas. The Institute have crow synth spies, so it is possible that they are capable of operating on a very large, possibly even continental scale, but they don't really need to so remain confined to the Commonwealth, only leaving when they have to in pursuit of escaped synths or the railroad, ie. Fallout 3. Could be the Institute are concerned about the rise of another major pre-war player, or even looking to cement an alliance with him.

Of course, they could also be scouts, sent east to survey the NCR, which they no doubt would be aware of, or Caesar's Legion, which could feasibly pose a threat to the Commonwealth one day. Both are major factions, the two largest we are aware of in the Post war US, and both capable of expanding to a point where they would be in direct contention with the Institute. I'm sure a group like that, which was so obsessed with controlling the progression of the commonwealth from behind the scenes for so long, would recognise the potential impact this would have on their future.

Either of those reasons could work IMO.

Well, as @"IRORIEH" said above, one of the major interests of the Institute in Nevada during 2281, would be Mr. House.
If this famous "Mr. House" they all talk about in Vegas and its surroundings happens to be the same man that had attended to the Institute of Technology 200 years ago, chances are that the Institute would be very interested in him. If it's in their interests to preserve Father's life, there is a high chance they would also be interested in the technology House used to maintain himself alive.