In our opinion, the best vantage point for a good snapshot of the Strip is from the Voodoo Lounge atop the Rio's main tower. You're about a mile west of the center Strip, which stretches from the far right (Mandalay Bay) to the far left (Stratosphere). Also, you're outside on a deck, so you don't have to shoot through glass. You can access the Voodoo Lounge for free most afternoons and early evenings.
A similar view, from a little higher up, but from a block farther away, is available from the Ghostbar at the top of the Palms tower. You can take your picture from outside. But you can't get up there for free.
The top of the Eiffel Tower at Paris, at 460 feet high, is also an excellent aerial. You're very close to everything, so it's a better view for detail (for example, of Bellagio's fountain shows) than for a panorama. There are small openings every few feet, so you don't have to shoot through the protective metal grillwork. There's an admission charge to get to the top.
The indoor and outdoor observation decks of Stratosphere Tower provide your highest view of the Strip. It's at the far north end, however, and the Strip takes a jog to the left between the Mirage and Caesars Palace, so it's best for shooting the north Strip (Sahara, Riviera, Circus Circus) and the Las Vegas Hilton. Admission charge.
Way down at the opposite end of the Strip, MIX is at the top of THEhotel at Mandalay Bay, on the 63rd floor. Dinner at this French-influenced restaurant is very expensive, but you can also go up and sit in the lounge on the 64th floor (admission). You can sit indoors or out but go up early, since the patio lounges are reserved after 10:30 p.m., though a small area is set aside for standing outside. Whether you go for dinner or drinks, make sure to check out the views from the stalls in the bathrooms.
You can also take a helicopter ride over the Strip. Papillon Helicopters circles the Strip nightly; prices start at $50 per person (plus a $5 fuel surcharge, which is currently in effect).