Now here's a kicker, if you are in a state where you can easily receive a license plate for your bike, then technically you are driving a motor vehicle, because many states have certain rules that apply to legal motor vehicles from different states, regardless of the type, especially mopeds as it would likely be defined in the home state, you could in fact get away with being grandfathered into the state as being legal. Like many states don't require of have insurance on the vehicle if the vehicle came from a different state and is still currently registered in that state, and the operator has a license or id from that state. As in you can get pulled over for something, and be uninspected or insured, and they can't say diddly squat.
I would say if you have interest, find out of course what you can do to make it legal in your state as a motor vehicle, if possible, then look at other states you might go into, and they're laws regarding the classification of your vehicle, and what the state you live in classifies it as, and the equivalent of the other state.
Remember that ignorance of the law is no excuse to break it, but cops are still people, and can empathize with you on a subject, legal or not, and if you are calm and make it known you honestly believe you are legal and quote sources, then you could get away with making that quick pass through that part of the state.
If you can determine it's a bad idea, then don't do it unless you're feeling very lucky.
In the city the police generally are looking for things out of place or things they are specifically trained to look for. If you look out of place then the police will probably pull you over just for that reason and wing the rest of it as it comes. If you act very lost then maybe you can get out of it but it's a s**t shot. Get familiar with where you are going and the places around where you're going. If they find you on blah street, say you were looking for a road nearly 15 miles north of you, or whatever is out of bounds of their territory.
Heck, say you were trying to find somebody to buy a truck/car from and say you're lost and the phone isn't getting good reception.
I'm not trying to advocate lying, but advocating being prepared to not get stranded 50 miles from home in a place you've never been before with your bike in an impound lot. Sometimes just saying you're just riding to see the view and didn't realize you crossed state lines, and promising you'll never come through on your bike again is enough.
Really though, research is the best weapon you have. And being friendly, bring friendly in a place where the police have way too much to worry about just shows them they have better things to do, and being friendly in a place where everyone's friendly and the cops rarely have anything to worry about just shows them you are not around for trouble but simply there to enjoy the fact that they are happy too.
Good luck, have fun, wear a damn helmet.