Actually, it depends on the state/city. There is no federal sales tax; all sales taxes are determined at the state and municipal level and are only charged at the final point of sale. Some states or cities allow for limited versions of what you're talking about; Washington State rebates sales taxes for Oregon residents.

However, why isn't this typical across all states? It turns out that taxes tourists is generally more popular than taxing residents. This is especially true if the tax is enacted by referendum. For instance, a lot of stadiums are publicly funded via hotel room and rental car taxes.