The OP was talking about editing, not quantizing. Any good DAW should have some sort of "snap" setting in the piano roll so that you can get MIDI notes right on the grid without quite some much messing around, but you can usually turn that off and just position it freely.
Most Quantize functions nowadays include a "strength" parameter that tells it how close to right on the beat you want it to move the notes. For example if a given snare hit lands 16 ticks before the beat, and you set Quantize strength to 50%, it'll move it 8 ticks closer to the beat. This can go a long way toward preserving a human feel while still tightening up the timing.
Also, a lot of times there's a window parameter that tells it to ignore anything that is too far from the beat. Most of the time quantization is like "rounding to the nearest". Anything that hits between a half beat (by beat I mean whatever beat size you're quantizing to) early and half beat late gets moved to that beat. The window can narrow that up so that, say, it only reaches out a quarter beat or whatever, and those other hits in between dont get "fixed".