I'm reading a thing that talks about US$3 in 1902 being about US$90 today. This is what an Inflation Calculator I googled up spits out, but in context this $90 is someone's seasonal daily wage before (significant) business expenses. Inflation alone clearly doesn't capture phenomena like increases to the cost of living, economic paradigm shifts like the increased prominence of money in our transactions (especially for basic needs), and really important consumption patterns that are hard to quantify (the person in question probably got most of his food from subsistence fishing and lived in a multi-generational home on land he may or may not have formally owned).
Is there a better way to discover and communicate the value of historical currency? Is trying to capture all of these in a single number just kind of hopeless?
You are right that inflation alone doesn't truly capture this. While inflation is part of it, there are a lot more pieces that go into valuing money in different time periods. To get a god sense of this, when valuing money in different time periods, prices of common goods such as staple foods and common consumer goods are looked at. Along with this the prices of houses/rent are also used, salary statistics, and even government documents (if available) such as unemployment assistance can be used. Instead of thinking of it as "value of certain currency" it might be easier to think of it as buying power. I don't have any specific sources, but I do have a history degree and this has been discussed in a number of my classes.