When you are talking about linear regs being noisy, what frequency band interests you? How many dB of attenuation do you require in that band?
Modern linear regulators have a humongous amount of attenuation for frequencies below 120 Hz. Even the lowly 78xx-series regulators have almost 80 dB rejection at those frequencies.
Higher frequencies for these regulators is another matter.
But if you require 120 dB at powerline frequencies, and 80 dB at 1 Mhz, I would use a LT3042. It also has a dropout of 350 mV while supplying 200 mA.