The gaming policies, night club policies, and liquor policies are VERY strict. 12AM on that night that legally starts your birthday local time. The hotel-casinos also tend to be very strict on policy and you should get an email for any exception about checking in.
The Westgate used to be the Las Vegas Hilton, and most Hiltons are 18+. Westgate changed to 21+. Call them, since depending upon where you look now, it still says 18, 19, or 21.
I think the Flamingo has actually two hotels, one of them Hilton.
This is 18+.
Caesar's Flamingo is 21+
When using a credit card you must check in with that card and you will need to be an authorized user at the bank records. They still require 21+.
It is OK to ask, and if they approve to get an email to show a printed copy at check-in, but I would not put my faith in it.
Booking.com and Smartervegas.com are usually two good pricing sites. Get logons for their better pricing.
In Las Vegas, book directly with the hotel and I think both of these do that.
The Riviera (closed and torn down), the Las Vegas Hilton (first non-renewed contract and then sold and revised to 21+), The Golden Nugget downtown STILL 18+
were the three gaming properties allowing 18+ Check-in leaving only one today.
The 2017 daily resort fee guide comes in handy:
That is a nightly fee per room per night. It is never included in Expedia and Hotel.com rates and hits you at check in. Flamingo adds $30 a night plus tax. Westgate says $29.95 (same thing).
The Elara is a beautiful 18+ at the back of the Miracle Mile shopping mall with Planet Hollywood in front. Wifi is extra, but no daily fee. If you gave the dates I could recommend an 18+.
You could do one night at the Elara and then change to the Flamingo at your 21st birthday.
Travelodge next to the Circus Circus is OK and 18+
Hilton Grand Vacation Suites Convention Center is 18+
Royal Resort was 18+ last I checked