From that particular part of Bellagio, if you are already standing outside, the answer might be Planet Hollywood. From Bellagio poker room, it's almost certainly Caesars. Paris and Ballys are also so similarly far away that I'm not sure what the practical use of this answer is (Ballys is actually probably the farthest of the four because the hotel is so far offset from the strip).
I actually made an account at wsop.com Nevada but the 4-5 deposit methods I tried didn't work. I read that you could fund your account by making a deposit at any CET property in Vegas. I play at Bellagio and normally take an Uber that drops me off at the main entrance. Therefore, that was my reason for asking. However, I believe I've found a temporary way to not have to make a deposit and at the same time this has given me an idea for a personal challenge. A couple days ago I entered a $25 free roll at wsop.com and came in 2nd out of 342 players. That paid a whole $3.56. I've then ran that up to $20.38 playing the 2NL tables over a couple days. This has given me the idea to see if I could turn that $3.56 free roll win into $10k by the end of the year.
I could definitely make more money playing live but I work from home and I have to be on the computer all the time so I rarely get to play live. When I do play live I put in some very long sessions. So far this year my shortest session has been 18 hours and my longest has been 34 hours. My average session for this year has been 24.6 hours.