hiking solo in a US National Park

You could take a look at REI. I believe they have hiking tours in all the National Parks.

Unless you pick a real remote, back country trail you will never be hiking alone in any of the popular National Parks. I have hiked in them and have never been really "alone". Getting trail photos without people in the way can be a challenge.

A lot of the parks have opportunities to hike with a ranger--free. Call the parks and request the "newspaper" to be mailed to you and ask about any hikes that they do on a regular basis.

Are you looking for just a day hike or a multi-day outing including camping or just looking for a series of day hikes.

If you are just looking for a hike or two, look around for hiking/outdoors clubs. For example, I'm a member of the Colorado Mountain Club and on any given weekend there will be at least 15-20 hikes going out and also quite a few hikes during the week. Since the Denver group is so close to Rocky Mountain NP, you may find a hike or two to RMNP. You can always tag along as a guest after signing off on the prerequisite waiver and based on the difficulty and strenuousness of the hike.

You can check out the CMC upcoming schedule here. https://www.cmc.org/Calendar/Trips.aspx

If you are headed to CA, check and see if the Sierra Club or other clubs have outings that may work for you.

Almost every national park has ranger led group hikes on a daily basis. You just show up at the assigned place and time and you have a group of people to do a short day hike with. There is no cost. I've been on plenty of these and they can be a great deal of fun and the ranger shares some interesting information as well.

Yellowstone has many of these types of hikes and a variety of accomodations. Just make sure that you have reservations for your lodging in advance.

Another recommendation to check for ranger-led hikes. Every park has a webpage with calendars describing hikes available on certain days. Here is the Yellowstone page as an example:
https://www.nps.gov/yell/planyourvisit/ranger-programs.htm

In Yellowstone and Glacier, and maybe others, hiking alone is discouraged because of bear issues. But a good point was made above -- in popular parks like those it's hard to be really "alone" hiking, unless you backpack pretty far in.

Ranger-led hikes are generally short and not difficult, always informative. Clubs like those mentioned can offer good company and experience. The idea of "an expert hiker" is a little strange, there are tips and techniques that are easy to acquire but it's really just walking on uneven terrain. More than that, it's backpacking or mountaineering or something like that.

I don't know who's writing now about hiking but I learned a lot reading Colin Fletcher decades ago. I doubt if there's much new that he doesn't cover.

Southern Utah is wonderful for national parks. I stayed at the very nice Arrowhead Country Inn, a B & B with cabins and rooms, and at least a few years ago, a fantastic breakfast. It is in the middle of the very beautiful and diverse Zion, Bryce and the North Rim of the Grand Canyon, located across the border in Arizona. (The North Rim is much, much less developed and commercial than the very popular and crowded South Rim.) each of these parks is very “user friendly” with a Visitor Center, rangers, and, I imagine, organized hikes. I would bet that many groups organize tours of this region, probably including hiking, such as Sierra Club, Roads Scholar (formerly Elderhostel), and others.

First, most of the National Parks have short hikes available on a regular basis, as mentioned above. You should be able to drill down into this looking at the websites for specific parks.

Second, REI has an excellent website showing hikes in the areas around their stores. This includes State and Federal lands, and often there's info on partnered hikes.

Come on out west, the parks are great!

What kind of hiking are you contemplating? There are plenty of designated hiking trails of varying difficulty and length in nearly all the western parks. The easy and medium trails usually have hikers on them all the time. They are mostly short hikes, none longer than about 6 hours. I don't have any experience with the difficult ones :-) Some are considered difficult because of the length and difference in elevation, not necessarily because they require special expertise. The rangers at the Visitor Centers can help you plan hikes that you'll be comfortable taking on your own as well as give you info on any/all ranger-led hikes.

Please check the Appalachian Mountain Club adventure travel (which despite name offers trips to different parts of the world) https://www.outdoors.org/outdoor-activities/adventure-travel and the Sierra Club https://content.sierraclub.org/outings/adventure-travel

Sorry - didn't see your original post as I was, in fact, in Yellowstone, lol. No cell service.

Now that it's been bumped I'll add that for Yellowstone there is a FB page for Yellowstone hiking that has lots of park/concession employees who are always looking for folks to hike with on their days off. If you are interested I'll be happy to link it.

I'd have to disagree with the statement about not worrying about hiking solo unless you are going backcountry. For Yellowstone this is not the case. The park service recommends hiking in groups no smaller than 3 due to the presence of bears. If you don't link up with a Ranger tour, you can wait at a trailhead and see if you can go with others who are headed out. FWIW, I carry bear spray even when I'm in the geyser basin around Old Faithful especially if I am out early in the AM or early evening. I will go solo in the geyser basins but won't hike on my own.