Aloha! 
I was wondering: Is it possible for a non-US citizen (visitor) to purchase ammo at a local gun shop? Or should I only buy it at the range?
I've heard Hawaii has pretty strict rules, so I want to make sure I’m doing everything legally. Any tips, range recommendations, or shop advice would be greatly appreciated!
Thanks in advance! 
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Hi,
I think the real question is whether or not (a) the range allows outside ammo, and (b) does the range you select have the caliber/type of ammo you want to use?
Some ranges don't allow you to bring your own ammo, or they will allow factory ammo but not ammo that was reloaded by someone who isn't licensed for reloading and reselling ammo in used casings.
A range's "no outside ammo" rule sometimes becomes a Catch-22, if they don't have the ammo you need/want in stock. Can't buy it there, and can't buy it elsewhere and bring it in.
So, choose the range you want to visit, then ask them directly if they have your ammo in stock and what the price is, as well as their policy on outside ammo. If they are okay with outside ammo, and theirs is more expensive than outside, you might want to call around to area gun stores for a better price.
Visitors will often choose convenience over cost savings anyway and just buy what the range is offering.
If you do buy outside ammo, or if you have some left over from the range, check the Hawaii statute
§134-27 Place to keep ammunition It has a list of lawful places you can keep/store ammo. It's basically the same list as where you are allowed to store or possess a firearm. For example, don't buy a box of ammo on the way to dine out. Buy it on the way to the range, at the range, or on your way back to the hotel you're staying in, or on the way to the airport (place of sojourn). It must be transported in a "Enclosed container" which "means a rigidly constructed receptacle, or a commercially manufactured gun case, or the equivalent thereof that completely encloses the ammunition." If that's an inconvenience or causes you to have to buy another case just for your ammo, then that adds another point toward buying ammo at the range and avoiding all of those Places to Keep rules.
https://www.capitol.hawaii.gov/hrsarchive/hrs2007/Vol03_Ch0121-0200D/HRS0134/HRS_0134-0027.htm