Riding my street legal mini bikes in other States, can I?

I live in Michigan.

I have 2 1970 Heathkit Hilltoppers that are legally registered as mopeds in Michigan.

Can I take them on Vacation and ride them legally in North Carolina and Tennessee?

I know you are not coming to South Carolina but in SC "moped" is defined as 50cc or less. You should be able to look it up on the NC DMV website. You might want to get it in writing from the NC Highway Patrol that it would be waved or grandfathered since it is a registered moped in another state.
I'm guessing it depends on who you are. If you're a wise ass teenager, then I would say No. If you are a more senior, polite person, and play dumb, you'll probably be alright.
like PAP said - be fast !