I’m not aware of any State that all ammunition alone is illegal.
Some States do have specific laws banning possession or transport of handgun ammunition or hollow points, but none that would apply to a box of 12-gauge shells or .22 rounds.
Massachusetts and New York both require a license. Basically in locations where possession of a firearm is restricted to licensed persons the ammunition is also typically licensed.
The exception is locations where only some types of firearms require a license to possess because the ones that don't require a license usually take the same ammunition as the ones that require a license. That doesn't happen in the US AFAIK.
As the other comment points out, there are plenty. For example, you must be careful not to accidentally drive into New Jersey as this poor mother did awhile back:
MA and NY both require a license to possess any kind of smokeless powder firearm. MA allows black powder without a license and I am not going to guess what NY allows.
Some States do have specific laws banning possession or transport of handgun ammunition or hollow points, but none that would apply to a box of 12-gauge shells or .22 rounds.