Would the Canon EF-S 17-55 f2.8 be a good lens for this need? This lens has excellent reviews and classifies the lens almost in the same league as an L lens.
It's a great lens, but in my experience f2.8 often isn't wide enough for a lot of work indoors without a flash. Also, if you prefer shallow dof portraits, 55mm f2.8 isn't really all that shallow.
Now, as to low light no flash it really depends on your individual shooting situation. What are you shooting? What is the lighting like? You can do some testing with your current gear to determine what exposures you're getting. Then it's simple math to find out what the exposure would be with an f2.8 lens. If you shoot mostly during the day when you can rely on sunlight coming in and you have relatively stationary subjects then it might be very good (although still not extremely shallow DOF). But if you don't have that good lighting or like to shoot in the evenings as well you may find the solution doesn't work. It's still a fabulously sharp lens. But it's your individual needs and environment that will determine if f2.8 and no flash is good enough.