I was charged rent for days I didn't reside in my rental unit. Can my landlord legally charge me for these days being I lived in a different state?

Do you have a lease? Did you vacate the unit?

I have a month to month lease. I was charged a full months rent though I moved in around the middle of the month

First, Please don't use the comments feature for follow-up. Use the Answer options

Second, ANY question on law needs to include your general locale as laws vary by area.

Read your lease. It will specify when rent is due.

As ScottGem Stated, read your lease... if the effective date was the beginning of the month you owe the full month. It doesn't matter how long it took you to move in... its all about what date you took possession on paper and were legally allowed to move in not when you actually got around to doing it.