How can I find out where to buy uncommon (for the location) items while traveling?

As you've mentioned in your question, online searches work best when you know the name of the store you're looking for, or what kind of store is likely to carry your item. I recommend instead you talk to a person.

If you're staying at or near a hotel, hotel staff are your first choice. The front desk, for example. These people probably live nearby, or are otherwise familiar with the area. They may know the name of the "foreign food store" where you can get peanut butter or something else that is exotic in your location. Or the name of the electronics chain, or the mall in town that has all the computer stores. You can walk into any hotel and talk to the front desk staff as though you were staying there (I've done this to get a cab in bad weather, for example.)

If you are a long way from a hotel, or you try them and get no luck, go looking for more humans who speak English. Staff in a coffee shop, perhaps. A library might be a gold mine. Look on the airport's web site to see if they have an information desk with a phone number and call them.

Still no luck? Go to one of your near misses. A food store that doesn't sell kale may at least know what it is and where you can get it. A hardware store than doesn't sell the odd part you need may again know the local name for it and a store that might have it.

After all of that, you will at least have gained some local words and names to make your online searches better. But I think it's more likely you will have found what you seek, or realized it's not obtainable.

Use your credit card's concierge service, if it's available to you.

At higher credit card tiers Visa, MasterCard and American Express all offer concierge services which can help you locate hard to find items, get hard-to-obtain dinner reservations or event tickets, and overall help with many issues you might run across while traveling. Just call or email the concierge and explain specifically what you need. This is available with Visa Infinite, MasterCard World and World Elite, and American Express Platinum cards.

This is exactly where a global network of Virtual Assistants come in handy, there are many many of them giving a global reach but local knowledge.

DISCLAIMER: I am the founder of such a company so I dont want to come across as pitching my services here on this site by posting links

Based on my own experience I'll still stick to Google, unless you are willing to pay more or have less of a variety.

I find that different concierge services or asking in groups and forums will be give you answers which are highly biased towards places they have used once, had one good (or bad) experience or get some commission or benefit from

painfully weed out online store, stores that don't have local inventory etc.

painfully is relative, it took me a few minutes to "find a laptop in Barcelona", and I had a more difficult challenge since I searched fro outside of Spain.

You will have bigger local inventory problem if you use "manual" search since many online sites can give you some sense about the local inventory.

As the thing you are looking for becomes more exotic simple search will take you further and faster, to get better results use the correct term in the local language, Google translate and other translation services will help you with that. So instead of "kale in Cancun" search for "comprar col rizada en Cancún"

As long as you're in a country where they have a presence, Amazon. (Note: I have no affiliation with Amazon.) Order with one-day shipping and you will have it the next day.

A tourist information bureau should be able to tell you the speciality stores in the area. They may offer to call them for you to check if they supply the item(s) you want, which can come in handy if your skills in the local language aren't strong.

In many countries there are offices dedicated to travellers. They usually provides infos about the city and nearby sites worth visiting. Their work is to help travellers by answering questions. The sort of questions, you are about to ask, are within their competence. At least they can suggest you some options where to get the final answer.

On the other hand, do not expect to get exact match. For example I've found one model of Vibram Fivefingers on their US-oriented e-shop but in CZ there was no chance to buy them that year - they were available year later as "new". You cannot buy any Skoda in the US while it's a common car in the EU. If you are looking for a Canon camera you can get one model with different names, so if your Rebel camera got stolen you will return to US with D700 model instead...

Also be aware that electronics are localized. In Europe the mains voltage is 230 VAC, in US it's 110 VAC. Different countries use different plug shapes. You won't get the not-localized plugs and powersources easily yet some producers offer some compatibility. For example the charger I got with my Canon D700 camera I bought in CZ is compatible with both 230 V/50Hz and 110 V/60 Hz power while the US-localized charger cannot withstand the 230 VAC power.

If you want to find out online, try to find an Expat online forum. There usually people have posted these kinds of questions (since they usually have exactly the same problem, trying to find specialized items without really knowing the location)

In general, I'd just ask someone who lives there! Especially if it's someone who sells other things in that category. That has worked dozens of times for me in Spain, Turkey, Taiwan, Korea, …

For the specific laptop example, I specifically wanted a MacBook. An employee of K-tuin (Logroño) ordered one with a US keyboard on Friday, and I picked it up at the store on Monday.

Not quite answering my question, but I've just learned that there is a service called Grabr.io, which lets you order items from the US, and matches you with travelers coming to your location, who will deliver the item "in 1-2 weeks".

Yet in the particular example of replacing my stolen X1 Carbon, this would've been the best option: order the thing from Amazon US, with a US keyboard layout, and have a traveler deliver it to me.