How do I apply for a Thai visa in the US without traveling to the Consulate?

There are numerous companies that will handle visa applications for you for most any country, although they will obviously charge a fee for their services.

If you are booking through a travel agency then asking them is generally the best place to start. They will normally have a specific agency that they work with, and will be able to look after most of the process for you.

Otherwise, there are countless companies you can deal with directly. Some of these only process visas for a specific country, while others will do most countries. Probably the biggest 3 names are (in alphabetical order) CIBT, Travisa and VisaHQ.

I have personally used Travisa many times (including for obtaining a Thai visa last month!), and can recommend them. However that's not to say that they are the best/cheapest depending on your specific circumstances.

You did not indicate the type of visa that you will be applying for. There are Thai embassies and consulates that will control the process for applying for a visa. Then there will also be Honorary consulates that have been granted special authority by Thai law (other countries have honorary consulates also) to issue Thai visas and perform other special consular duties.

For single-entry Thai visas, it might be more efficient to use an honorary Thai consulate. There are several of them scattered throughout the USA, and most of them will accept applications via overnight mail. Honorary Thai consulates worldwide no longer issue multiple-entry visas of any category after August 2016. You must go (or in some cases mail) to the Thai embassy or a Thai consulate to obtain your visa. Or you can use a friend to drop off the visa application and pick it back up (basically doing what a visa runner agent would do). You shouldn't need a limited power of attorney, but it may not be a bad idea.

Or you can also use visa runner agents and such, but in a place like the USA I would check a few honorary consulates first like Dallas, TX or Portland, OR. I might use an agent in a place like Penang, Malaysia because the price is reasonable and you actually save 2 trips.

There are online services like VisaHQ that provide online application for Thai visa, so I am not sure that there is any reason to visit NYC for that particular purpose.