Do I have to take the NCLEX in the state I graduated from?

You should plan on taking the test in the state where you plan to work, unless both states are compact states, then it would make no difference where you take the test and are licensed. (As others have said, the NCLEX is a national exam--it's the same test no matter where you take it; it's called the National Council Licensure Exam.)

Compact state licensing allows a nurse who is the resident of one state to practice in any of the other agreeing states. In effect, you have a multi-state license that allows you to work in any of those states (The entire list of compact states is: Arizona, Arkansas, Colorado, Delaware, Idaho, Iowa, Kentucky, Maine, Maryland, Mississippi, Missouri, Nebraska, New Hampshire, New Mexico, North Carolina, North Dakota, Rhode Island, South Carolina, South Dakota, Tennessee, Texas, Utah, Virginia, and Wisconsin.)

In your case, Michigan is not a compact state, so if you took the NCLEX in Michigan you would have a Michigan nursing license. When you move to Texas, you'd apply to have your license transferred to Texas and would not only have to pay another $150 to $200 (depending on the cost of that Texas license) but you'd also have to pay a fee to Michigan (usually approx. $50) for their BON to verify your license to the BON of Texas. As you can see, this could add up to around $400, while obtaining a license in the state you intend to work would cost just that state's fee. The advantage of holding a Texas license (or a license in any compact state) is that your license allows you to work in another compact state without paying additional fees.

You should plan on taking the test in the state where you plan to work...so if you took the NCLEX in Michigan you would have a Michigan nursing license.

Thats not true. You dont have to take the test in the state you plan to work. And taking the test in a particular state doesnt mean that your license has to be in that state. You can take the test anywhere you want but you just have to apply to the BON in the state you plan to work in.

Me for example: I live in Ohio and am going to take my test in Ohio. But I applied for a Texas license, therefore Pearsonvue will be sending my NCLEX results to the Texas BON.

What Patty_RN is explaining is no longer the case. I learned from a nurse at work though that thats how it used to be done.

Actually, I just applied for a license in another state and went through the application process, paid for that state's license and also paid for my BON to endorse (verify) my license. The total cost was close to $300--not including the license I have from my state of residence. This is EXACTLY the process. While it's certainly possible to take the exam in one state and apply to a different state's BON, this doesn't seem to be what the OP was asking (in fact, you could even make a little vacation out of taking the NCLEX and go to Japan, Australia, Guam, or Puerto Rico for the purpose of a domestic license).

As far as license transfers, the following is an accurate guide:

A Complete Guide to Transferring Your Nursing License to Another State | The BSN to MSN.org Blog

Nope. I went to nursing school in state A, took the boards in state B (closest place at my time of choosing), and got my license in state C. Passed in 55 minutes with 75 questions...

....and now I would probably fail if I took it now. When watching a medical tv show and see the heart rate in the 50s, my NICU instincts made me jump, "CPR!!!!!!!!"