It’s the “Taj Mahal Palace and Tower Hotel” and the tower is the new part of the hotel that was built in 1973. From photos I’ve seen it seemed like the tower had at least 20 floors but I don’t know if that’s what the report is talking about.
Yup, the tower part of the Taj Mahal seems to be around 20+ stories:
http://en.wikipedia.org/wiki/Image:Exterior-_Gateway_View.jpg
Not saying there are hostages on the 19th floor there, I have no idea, but that tower does seem to have at least 19 floors.
Brit at the Taj said 30-40 diners from resteraunt herded into stairwell while he slipped away, focus on US and UK passports, also tens(?) of EU politicos at hotel for EU/India summit holed up, current status unknown.
http://www.usatoday.com/news/world/2008-11-26-india-shooting_N.htm