Does Airplay allow me to connect an iPad to the HDTV in my hotel room when I am traveling so I can enjoy a movie on a large screen?
Well i travel extensively and I rarely am in the room watching movies, however If you bring the wallet sized AppleTV box, then you get to enjoy the nice wireless experience of Airplay. That way you're not having to sit 6' away from the TV, or have to jump up off the bed every time you want to pause or rewind something.

If you're dead set on tethering your tablet to the TV via HDMI via physical cable then yes, you have to come off a whopping $28.

If I had an iPad with retina display I'd likely rather watch the movie on that screen. Likely a much better picture than the in-room TV.

That said... the MAJORITY of the "streaming" i do from my iphone or ipad is at home. Music, videos, etc... that thats much much better through airplay. I can have my iphone in my pocket, adjust playlists, songs from anywhere around the house. Cables are a dying breed. Old technology.