Can anyone recommend ways of finding out about low cost / direct impact things like this? I'd much prefer to fund a specific laptop than throwing money into the void of big charities.
I found catholic charities to be best for this (I am not catholic). They work on site, have long tradition and very small overhead.
Find local people in your area. Religious communities are a good place to start, especially if you have any sort of affiliation yourself. There might be refugee focused charities or community groups, PC recycling charities.. Shouldn't be hard to find. Call them. Ask what they need or tell them what you'd like to do.
Other than PCs (and other material things they need), it can be good to just have newly arrived refugees to dinner. It helps to know local people like you personally.
https://www.facebook.com/computersforrefugees
I've been thinking about setting something like this up where I come from in London, UK. A worker at a refugee centre told me that laptops are an extremely helpful tool for refugees so they can communicate with authorities and aid agencies in good time, but that they were out of reach for most. Refugees generally have stupidphones because they're cheap and easy to get a hold of, but not laptops.
Anyone interested in working together on something like this in London?
[1] https://www.givedirectly.org/ [2] http://www.givewell.org/
As an aside, the costs are actually representative of the treatment, unlike in the inflated world of American insurance.