Hourly room rental

Is there such a thing as hourly room rental in New Orleans?

I have sugar daddy kind of informal relationship with a younger woman that's been going on for a while now. We're both married so our homes are rarely an option. At first, we'd see each other less frequently but for long multi hour dates (6-8 hours) so hotels were the obvious choice. But over time the relationship has changed into more of a mistress scenario and we want to see each other more frequently, just for an hour or two during the day, whenever possible.

Hotels, with their 3 pm check ins and 11 pm or noon check outs, are expensive and inconvenient. Are there hourly room rentals in New Orleans? Something was available on a spur of the moment would be ideal.