Some forests in the Western United States will have been logged at different times and by different methods i.e. clearcut vs selective logging.
As time goes by, the trees will grow back but this results in different environments and amount of wildlife as well as some areas being easier to hike with less deadfall on the ground.
Are their historical maps of when a forest in the US was logged?
In the US prior to about 1900, there was little control over logging. Around 1900 the practice of Reforestation began gaining tracktion, with more oversight and controls.
Forest that have never been logged are called "Old Growth" or "Virgin" forests. Wikipedia has a list of US Old Growth Forests these will have never been logged (I am going to ignore selective harvesting as healthy management practice for simplicty)
As a partial answer, it is relatively easy to find one of the few areas that have never been logged.
In my experience being under the canopy of a forest area that has not been logged in ~50 years is very similar to old growth. I think the key you are interested in is mapping logging in the last 50 years.
This question intrigues me, so I have been looking for maps of logging, and I am not finding any. Here is a guess on why they may not exist.
@JamesJenkins answer is pretty good. I'll add two points based on my experience as a forester. I think the 2nd point especially will help you find the info you're looking for, which is, TLDR: Forest stand maps can be very useful for planning woodland activities, serving as a great clue about where you'll find different types of forest structures and dynamics.
1) How long it takes for forests to reach a stage in succession that feels like old growth depends on the forest type, and while ~50yrs is a decent estimate, some areas may take much longer or shorter. In some cases, no amount of time will lead the ecosystem into a similar dynamic as it originally had before human disturbance. That could be the case in the USA's west where massive trees were removed on steep slopes prone to erosion, but I'm not so familiar with those western woodlands.
2) If logging is done by an institution that needs good accounting/bookkeeping, e.g. a timber investment management organization (TIMO) or government land owner (e.g. USFS), they should have a pretty good forest management plan going forward and record of the plans and timber sales from the past, at least since they started record keeping. For gov't lands this is probably public info since it's public property.
Info about forest management (including logging) would be organized by forest stands. These are essentially management units, areas mapped out based on similar species, size, age class, or other distributions. Records would show what stands were harvested when and using what silvicultural prescription, and how many million board feet (MBF) of wood was sold in different grades/quality classes. Ask the local office in charge of the lands you're interested in about forest stand maps and harvest records and see what they say. If you're not sure who manages that land, you can start at your most-local department of environment agency (e.g. NY DEC, NH DES, PA DEC) and if you're clear and polite about what you're looking for I bet they'll point you in the right direction as best they can.
