Because sales tax from a restaurant passes through to the state do I include it on my income statement and then write it off as an expense? Or do I leave it off both sides (income and expense). Which is the more correct way to handle it?

In your trading account you should net the sales tax account (debit)
With the sales account itself (credit).

Where are you at? Since you mentioned it passing through to the state, are we speaking of United States?

If so, it's not an expense. You collect it from the customer as it is their expense, not your company's. But since the company is the one who has to pass it along to the state, it's a liability.

For instance, if something is $10 and you add 5% sales tax, that's $10.50 total. You dr cash 10.50 for what was collected, cr sales only the $10 (because it's not income), and then .50 cr into sales tax payable. You'll dr it back out of the payable when it's paid. No income/expense involved at all.

In my state only drinks are taxable though. I worked at a restaurant for a time and in the bar, the price included the tax. (That is typical around here, so to the customer, the price stated is the price.) In that case, I had to back out the sales tax to get back to the actual sales price. Using the 5%, I would have divided by 1.05 to get back to the original cost.