(Un)beaten hiking paths in the US?
 

I am looking to make a hiking trip soon to somewhere I can physically test myself. My actual hiking experience could be higher, but my physical (especially carrying weight on my back) fitness is no problem at all here. Any suggestions?

Riddle me this. . . How can a hiking path be unbeaten>? Is it not a requirement for a path? Trail?

It sounds like you're looking for a dayhike rather than an overnight backpacking trip.

In that case, hike to the bottom of the Grand Canyon and back up in a day. Great test of your physical fitness. It is not at all off the beaten path. I would not suggest doing a really strenuous hike to test yourself on a remote trail, definitely not on an off-trail route given your lack of experience.

I suggest the book 100 Hikes/travel guide Central Oregon Cascades by William L. Sullivan. Many of the 100 hikes will fit your level of fitness. Hiking at elevations above 4000' is tougher than below 3500'.
I have hiked several sections of the Pacific Crest Trail but unless you have a partner to move the vehicle ahead, you have to turn around at some point in the early afternoon to get back by sunset. Be careful if you decide to camp along the trail since bears will be attracted to your food cooked or uncooked.

You'll have to be a little more specific. Well, actually, a LOT more specific.

1) In what part of the USA are you thinking of hiking?
2) Are you thinking of a day hike, an overnight trip, or a week-long backpack walk?
3) What, exactly, are you trying to "test"? Speed? Endurance? Climbing ability? Survival with minimal gear?

As others have noted, I strongly suggest you NOT hike in a remote area to "test" yourself, simply because you won't just get a bad grade if you "fail" -- and how could it be a real "test" unless there is at least the possibility of failure? Stories like Into the Wild might seem romantic to you, but the simple fact is that Christ McCandless was DEAD at the end.
I've hiked over 1400 miles on the Appalachian Trail, all solo, not as a test but simply because I love the challenge of back-country hiking & backpacking. I've also done day hikes in over a dozen national parks. If we could get a clearer focus on what, exactly, you hope to attain in this "test," we could give you a much better answer on where you'll find the chance to do so.

Virtually any sizable National Park or Wilderness Area in the U.S. would fit the bill.

While you are there please spend some money in the neighboring communities so they reap an economic benefit.