They're not traditional omelets, but my vote is for Charlie's Sandwich Shoppe. Gigantic and delicious. Especially the spinach and feta or hot sausage, pepper and onion.... damn.
If you do a search, you'll find a thread from awhile back that I believe I started about omelettes. My complaint is that most places overcook omelettes. The best omelette I ever had was at Wheatleigh, in Lenox, but I suspect you're not interested in driving 2+ hours and paying Wheatleigh prices on a regular basis. In Boston, I've had decent luck with omelettes at Brasserie Jo and (believe it or not) at the Stanhope Grille at Jury's Hotel (where you can get a made-to-order omelette as part of their $18 breakfast buffet).
Not downtown Boston, but I like the omelettes at Ball Square Cafe in Somerville. Inventive combinations expertly prepared. Only open until 3:00 and it gets mobbed on weekends.
Ball Square Cafe
708 Broadway, Somerville, MA 02144