No. When Bellagio opened in 1998, Las Vegas was already abandoning the "family destination" marketing spin of the early ‘90s and Steve Wynn set a new precedent by initiating a no-children policy at his new property. This meant no one under 18 was permitted unless they were a registered guest of the hotel, had tickets to a show, or were in a party with reservations at one of the property’s fine dining establishments.
At the time, the PR spin on the no-kids rule was that it was to avert overcrowding on account of the overwhelmingly popular demand to look around the new hotel, although it’s more likely to have been due to the desire to achieve a sophisticated adult ambience throughout. Although a call to Bellagio’s PR department concluded that the policy is still officially in place, though it’s certainly no longer enforced and kids and strollers are now welcome. Likewise, the other properties in what was previously Wynn’s group – Golden Nugget, Mirage, and TI – no longer have the no-stroller policy that was in place under the former owner.
Wynn Las Vegas, Steve’s new property, permits children of non-guests to visit but strictly enforces a no-stroller policy (although on a recent visit, an LVA staffer saw a stroller complete with kid and pregnant mom pushing). Interestingly, the Borgata in Atlantic City, begun under Wynn’s aegis but sold to MGM in 2000 along with his other properties, also opened with a no-under-18s policy, which remains in place today (with the exception of hotel guests).
Of course, all casinos are bound by Gaming Control regulations dictating that no under-21s should stand around in gaming areas, and many shows and some restaurants are restricted to those 18 years or older.