I've probably shot more images on full frame cameras with an EF 24-105mm f/4 L IS than any other lens. But for what you want to do in low light, it's not the best choice. At f/4, it's just a bit too slow.
I'd suggest a 24mm, 28mm, or 35mm prime lens. While 24mm f/1.4 primes can get expensive because they are such a challenge to design and produce well, there are more than a few affordable 24mm f/2.8, 28mm f/1.8, or 35mm f/2 lenses on the market. Compared to your old crop body, 24mm would give the same field of view (FoV) with the 5D Mark III as 15mm does on your Rebel T2i/550D. 28mm on FF translates to 18mm on the 550D, and 35mm on FF is the same FoV as 22mm on a 1.6X crop body.
Another great option would be the EF 16-35mm f/2.8 L III, but it is even more expensive than the EF 24-70mm f/2.8 L II. The earlier versions of the 16-35/2.8 L are not near as good optically as the "III", or as the more economical EF 16-35mm f/4 L IS (if one can do without the f/2.8 maximum aperture). For wider landscapes using a FF camera, including cityscapes at night, the 16-35/4 L is a great lens. But I think you'll find it not fast enough for group portraits in low light.
If your budget doesn't allow for the EF 24-70mm f/2.8 L II and you are dead set on a zoom lens, my advice would be to go with the less expensive Tamron SP 24-70mm f/2.8 Di VC. It's sharper than the original EF 24-70mm f/2.8 L (which I still use because it gives me what I need for a 24-70/2.8), but not quite as sharp as the newer "II" introduced in 2012. The Tamron also offers something the Canon does not: Vibration Compensation, which is Tamron's term for 'Image Stabilization'. I've got several friends who have the older version of the Tamron, and they are extremely happy with it. Tamron just released a 'G2' ('Generation Two') update a few months back that adds the ability to update firmware and calibrate AF using the Tamron 'TAP-In' USB dock. it is currently selling for a little more than the older one was before it was replaced, but it is still several hundred dollars cheaper than the Canon EF 24-70mm f/2.8 L II.