I received a request to list the best Las Vegas night views. Typically their found in the hotel rooms but several attractions and bars have them as well. The Mixx at the Delano has this view of Las Vegas at night. One of the best "mostly" free views but it never hurts though to order a drink and enjoy it. Another great view is the view from the north end of the strip at Stratosphere, 1,149 feet high but this one will cost you $18. Closer to the ground you can't go wrong catching the Bellagio Fountains day or night for free. Lets hear your favorites!
The Eiffel Tower and the Stratosphere Tower are good spots but like you say booking a hotel room with views of the Strip will allow you good views too.
My favorite one is VooDoo at the Rio. You can also get great shots from the pedestrian bridges that cross over Las Vegas Blvd: 1) Bally's to Caesars 2) Cosmo to Planet Hollywood and 3) MGM Grand to NYNY
I think one of the best ways to get a superb view of Vegas is on a helicopter ride over the Strip at night. Pricey, but well worth it!
Go to any bar or lounge like Voodoo Lounge, Foundation Room, Ghostbar, or Moon. Be4st views you will get are from any of these places. I particularly like Moons at the Palms because of the glass-floor balcony.