I've tried the liberty inn but both parties have to show their ID and they don't allow guests to go up to the rooms. Otherwise, that would be an excellent choice but most guys don't want the hotel to keep a copy of their license.  Are there any places available in the mornings that are short-term or reasonably priced? Thank you

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Years ago, and I won't saw how many, I registered as the President of the United States (I won't say who was POTUS at the time) and they didn't bother to check my ID.  I was going to tell them that my associate was part of my Secret Service security detail but they didn't even bother to ask.  

Times change. I hope they changed the sheets, too

You are funny!

Rates are no worse than Liberty Inn, some let you check in as early as 7am, and they do not require ID from guests (you check in, but they can simply come up and visit, same risks as an overnight hotel stay). If you don't know what I'm talking about, just google "day use hotels nyc" and you'll see what I mean.