Rockhillmanor brings up an interesting point. As a full-timer and a firearms instructor (NRA and Utah BCI) I deal with this on a daily basis. It's not as hard as it seems, even though it could easily appear overwhelming.
The app I recommend is called Legal Heat. It has good information on the firearms laws of all 50 states, and reciprocity/recognition maps for the permits from each. Reciprocity and recognition are two major benefits of a good Concealed Firearm Permit for full-timers.
Reciprocity is a formalized agreement between two states indicating that the permit for one is valid in the other. Recognition does not have a formalized agreement, but is still valid in the eyes of the law.
For the Utah permit, for example, Utah has Reciprocity with:
Alabama
Alaska
Colorado
Florida
Georgia
Louisiana
Mississippi
New Hampshire
North Carolina
North Dakota
Ohio
Pennsylvania
South Dakota
Texas
Virginia
Washington State
West Virginia
And recognition with:
Arizona
Arkansas
Delaware
Idaho
Indiana
Iowa
Kansas
Kentucky
Maine
Michigan
Missouri
Montana
Nebraska
Oklahoma
Tennessee
Vermont
Wisconsin
Wyoming
That's a good portion of the USA. A few have a caveat that it must be a Utah permit held by a Utah resident, but that's OK. It still allows me to travel across the USA being legally covered.
What scares most people is that when you are in the other jurisdiction, you are subject to their firearms laws. The Legal Heat app gives you an overview of prohibited places under each permit - that's the biggest thing. Each state may have different restrictions on where you can take your concealed firearm.
As long as your permit is valid, you should generally not have any issue just driving down the road.
One advantage in Utah is that - in Utah - it is a Concealed FIREARM Permit. In Utah, as long as you can conceal it, you can carry it. I can carry a PS90 under my coat if I want. I can also openly carry it too, although open carry isn't something I generally recommend. Outside of Utah, permits often only cover handguns.
I also hold a Nevada permit. This allows to me to carry in Nevada and New Mexico, but no other benefit. When I got mine, they made you take a shooting test with whatever you want to carry. Now, the shooting test only requires you to shoot one firearm to carry any handgun.
I don't generally travel where my permit is not honored. It means that some trips might take a little longer as I avoid those states where it is not valid, but I spend money in places that allow me to defend my family if required. Freedom is worth it.