If you have a permit to have a gun in Virginia then you can carry in those states that have offer reciprocity to those with a Virginia permit. Your permit would be honored in Alabama, Alaska, Arizona, Arkansas, Florida, Idaho, Indiana, Iowa, Kansas, Kentucky, Louisiana, Michigan, Mississippi, Missouri, Montana, Nebraska, New Mexico, North Carolina, North Dakota, Ohio, Oklahoma, Pennsylvania, South Carolina, South Dakota, Tennessee, Texas, Utah, Vermont, Virginia, West Virginia, Wisconsin, Wyoming.
The laws of the individual states must be followed as to where, when and how you can carry. You can familiarize yourself with them on a site such as this one.
If you have no permit, then the site above I just linked you to will give you the car/carry law for individual states.
I assume that when Virginia restored your state rights that you had your Federal rights restored as well. If you do not know if that's true, you don't want to transport firearms out of state as you would be in violation of Federal law.