Yes, you may set up different sales tax rates for different locations.
On the "Places You Lived" page, set up a separate line entry for each sales tax rate (click on screenshot below). The state can be the same, but the dates must not overlap. For the general sales tax calculation, set up one location for each span of dates with the appropriate sales tax rate for that period.
You may enter multiple major purchases for each location as long as the sales tax rate is the same.
The easiest way to find this section of TurboTax is to search on "sales tax deduction", then click on the "jump to" link to go directly to the start of this topic.