Depends on the definition of "proximity" but I like the ones at the Sigma Derby @ MGM....spicy (but not too much) with two olives and a lime wedge and they come quick.....
First Food and Bar (Sorry not to provide a link, but for some reason it puts my posts in jail pending moderator approval) has a bloody mary cart rolling around during Sunday Brunch. $10 each, and you can get a free one if you bring them a hot sauce that they don't have. "The best Bloody Mary" then devolves onto you, but it is great fun looking for it.
I second Money's suggestion of First Food. I had the bacon infused Bloody Mary in August, also Sunday brunch. One added bonus, the wait staff are dressed as tarted-up school girls.
Have stayed in Bally's, Paris, PH area plenty of times. Baccharat Bar at Bellagio best I have had. They make their own mix.
I have been told by my favorite aunt who is quite the bloody mary drinker that the comp bloody mary's @ Aria are very good as well as the ones for purchase at Todd English Pub @ City Center/Aria.
Cheap but good Try out the $1 bloody mary's breakfast specials over at la salsa catina in the Planet Hollywood mall complex. They use a very good homemade mix, pretty stout on the vodka and the spice is dead on great. Plus you can get a fantastic Mexican breakfast for $3 as well.
BMs As a BM (I mean Bloody Mary) Aficionado, I agree that Sully's Bar at Bally's makes a very good one. Definitely ask to have them make it with Absolut Peppar vodka (still comped when playing VP). IMHO the best BM on the strip is at Bellagio. Best downtown is Golden Nugget. Chris