Mon Ami Gabi is a must if you are looking for a great brunch place. It can get a bit toasty, but the patio is the way to go. You get to enjoy a Parisian ambiance with a view of the Bellagio's water fountain show. If you're worried about the heat, the staff has you covered. They are very attentive and will make sure you always hydrated.
I would highly recommend the eggs benedict. Another honorable mention is the steak tartar.... The burrata and tapenade was also pretty good, but the tapenade stole the show.
Enjoy!