Things to consider first
The first thing you need to consider is whether the Xiaomi model you want to buy is going to work on your carrier's LTE frequencies. Not all Xiaomi phones have the right 4G bands to work with American carriers, so make sure you do that little bit of homework before you pick one up.
Also note that the Google Play Store does not come pre-installed on Xiaomi devices sold out of China, so be aware of that before you invest in one. Of course, Xiaomi devices sold in some markets do have the Play Store installed and there are ways to get it installed manually. Just keep that in mind when picking a website through which to buy a Xiaomi device.
Where to buy Xiaomi phones in the US/your country ?
The first place to take a look is mi.com where you can choose your delivery country from a drop-down list and see what devices and accessories are available in your region.
Once you know you want to buy a Xiaomi phone in the US the next step is to find an online retailer that sells it. You can always check Amazon.com or eBay.com to see if either of those sites have offers available, but your best bet is to look up one of the larger retailers that will ship a Xiaomi device to the US. Please note that some retailers charge extra for delivery to the US.
Newegg.com is one of the most popular online retailers through which to buy Xiaomi devices. Stocking a ton of Xiaomi devices, Newegg is a great online retailer with some massive discounts available. For example, you can pick up a Xiaomi Redmi Note for just $169.99.
Oppomart.com is another massive online retailer for not just Xiaomi devices, but other hard-to-get phones like the OnePlus 2. Oppomart regularly has online sales too, so you can also pick up a Xiaomi phone on sale. For example, right now you can get the Redmi Note 2 Prime for just $199.99. Not bad at all.
TinyDeal.com is another massive Chinese online retailer worth checking out as they too deliver to the US. They even have en English language website which is nice. Right now you can score a Redmi 2 for a crazy low $97.40.
DHGate.com is a great online retailer that offers free shipping to the US and progressive discounts on larger orders. For example, you can buy one Xiaomi Mi 4 for $250.00 or two at $240.00 each. Three will only cost $233.00 each and so on.
Banggood has a nicely set up site in English and also ships to the US. Banggood is also well known for offering heavily discounted phones, including those from Xiaomi. Right now you can grab a Mi 4c for as little as $259.99.
Flipkart is a huge online retailer servicing India. Officially Flipkart doesn't ship outside India but India is a wonderful country with many options for getting things delivered to (and forwarded on from) an Indian address. Of course, this method isn't anywhere near as secure and sure-fire as some of the other options, so perhaps use this as a last resort (unless you have friends in India).
Geekbuying.com is the last on our list of reliable places to buy Xiaomi phones but it certainly shouldn't be considered the worst choice. Geekbuying has a great reputation and also offers Xiaomi phones at heavy discounts. You can score a Xiaomi Mi 4 for just $239.99.