What is the fastest way to travel from the NE states to Michigan without going through Canada?

Fly.

I-95 to I-80 to Ohio Turnpike then up to Michigan

Well, it depends on where in the NE you're departing from. I traveled from Newburgh, NY to Kalamazoo, MI. I took I-84 W to I-81 S (towards Wilkes Barre, PA) to I-80 W (towards Bloomsburgh - you'll have to pay toll) to I-69 N (towards Lansing) to I-94 W (towards Chicago) to I-94-BR into Kalamazoo. That takes about 11 hours, to get from NY to MI, and you don't go into Canada.

I90 thru NY state, down and around Lake Erie, then depending on where in MI you want to go depends on where you get off I90. I75 goes into Detroit, I69 goes into Battle Creek

Find I-90 and run it to Toledo, Ohio...from there you can get anywhere in Michigan, like Detroit, Ann Arbor, Lansing Jackson, and points northward...I-75 is the 'backbone' of Michigan...just remenber to watch out for traffic and crazy drivers in Cleveland