Go to
http://www.tires.com" onclick="window.open(this.href);return false; or
http://www.tirerack.com" onclick="window.open(this.href);return false; They have applications that can show you all of the optional tire and wheel sizes that will fit your car. You will have to buy new wheels for about $100+ each, plus tires for about $100+ each, so expect to spend $800-1200 or so depending on what you want. On the base Vibe, 16" wheels were standard, 17" optional, and 18" are on the 09-10 GT models. Any of them can use the 16" wheels and appropriate tires. The only difference as SeattleJeremy said is the engine size, as they have different bolt circles. Wheels from a 1.8L will not bolt up to a Vibe with the 2.4L engine, and vice versa.
Since you are saying low profile tires, I'll assume you have a 09-10 GT. Stock size is 215/45-18. You could change to a 205/55-16 or a 215/50-16 tire on a 16" wheel. Of course, you can just go to a larger tire store and have their sales people show you all the options and help you select the right sizes. They will have all the info on what will fit.
Good luck!