I live in a state that now collects sales tax on internet purchases. If I order something from Amazon and have it shipped to another state,what state charges sales tax,the state I live in or the state where it's being shipped?

I think it's where you live, but you can find out at the submit order screen I imagine.

Also, legally, you still have to pay the tax come April.

It's the state where it's being shipped. Amazon just started charging sales tax here within the last couple of months, but before that, when my friend would order stuff to be shipped to his parents in Kentucky, he would get charged tax, whereas if he ordered it shipped here, he would not.