Hotels are great for certain things, like getting some rest. They're also very good at getting you to pay for pretty much every convenience. Want "deluxe" wifi? That'll be $10. Want to enjoy those M&M's? That'll be another $7. Interested in kicking back to a nice movie? You can use our TV's in-demand system! $6, please!
Most of those fancy hotel TVs have HDMI ports, however the ability to switch inputs is disabled completely. That means the media on your tablet, adapter, and HDMI cord that you brought are a less than worthless. Holding your tablet is fine, but keeping it propped up can be a pain if you don't have a stand. You can, however, make your own serviceable stand using common hotel room items. Just take a hanger from the closet, a drinking glass or other piece on the heavy side to hold the tablet up and the hanger back down.
Short version: Make a make-shift tablet stand with a hotel hanger and a drinking glass.