Can I help you? On Twitter, the answer is no.

Objective: Find a hotel in Nebraska with wireless, a pool and a gym.

Twitter: Tweeted @HyattConcierge at 11:57 and got a reply at 12:42 informing me that there are no Hyatts in Nebraska.
Time: Almost an hour
Problem solved? Mostly.

Phone: After a few minutes of excruciating hold music that included the lyrics "you will fall like a feather into my lovin' arms," I was patched through to a human. He told me that there were no Hyatts in Nebraska, but that the nearest alternate location with a pool would be the Hyatt Place in Des Moines, Iowa. He also offered to book me a room.
Time: 4 minutes
Problem solved? Yes

Website: Sent an email at 12:53 p.m. and got a response at 7:45 p.m. The email said that it was a pleasure to assist me, but that "unfortunately, at this time we have no Hyatt Hotels in Nebraska."
Time: Almost 7 hours
Problem solved? Mostly.

Verdict: With Twitter taking almost one full hour--and e-mail taking almost seven--the phone was the quickest and most thorough route.