What options do I have for extending my stay in Thailand after my 60-day stay without a visa?

As a US citizen currently in Thailand with an initial 30-day stay followed by a 30-day extension, you have several options once your extension is over. You can apply for another 30-day visa exemption, but this would generally require you to exit Thailand and re-enter. Alternatively, you could consider applying for a tourist visa at a Thai consulate, which could grant you a longer stay.