Shop without paying sales tax in US?

No, in most states you are required to pay sales or use taxes on your purchases based upon where you live, not on where you buy things. If an item is tax-exempt where you live, and you purchase by phone, mail, online or by traveling out of state to buy it and bring it back, then it is tax-exempt in your home state.

However, regardless of where you buy something, if it is taxable in your state of residence and you bring it into that state or have it delivered in that state, then you still owe sales and use tax on that purchase, just as if you had purchased it from a local retailer. Some states make it easy to comply with this requirement by allowing you to file an annual return and sales and use tax payment with your annual income taxes. Other states require you to pay the sales and use taxes within a very short time of your out-of-state purchase.

Failure to pay sales or use taxes on things you bought out of state is a form of tax evasion, which is a crime.