Can a US citizen on a tourist visa re-enter Thailand after a short trip to a nearby country?

If it is a single entry visa then it is already used.

You can keep the same "admitted until" stamp with a re-entry permit.

However, if your current stay has less than 30 days to run, leaving and returning will get you a 30 day visa exempt entry anyway.

As Ellie said you can apply for a re-entry permit. But if you will have 30 days or less left of your original entry stamp when you return, there's not much reason to spend the money on a re-entry permit since you are eligible for visa exempt entry with a US passport which will give you 30 days. But if your plan is to travel to return to Thailand via land border from this nearby country, you need to make sure you haven't already entered Thailand 2 times at a land border without a visa, since that's the limit (at a land border only).

Yes, but you need to apply for and get a re-entry permit BEFORE you leave Thailand. And no additional date further than the current permitted-until-stay date.

This is general information on re-entry permits.