LM317/337 are cheap and quiet too (with a capacitor in the divider).
afaict from a quick look at datasheets LM317 is much higher noise than LM7808
Yes you are right. @imo: 
Well.. LM7808 is obsolete. Modern version is UA78M08, 40uV RMS noise. LM317 have whooping 240uV RMS. MC7808 (from ON semi) have 10uV RMS.
Always doublecheck info from public forum where anyone can convincingly say anything.
Well, imo's comment was quick and inaccurate, but as I said above, there's still a reason why the LM317/337 was a favorite in many audio applications compared to the 78xx line, so maybe that's what he was remembering.
Yes the typical RMS output noise of the LM317 is higher (although I think they don't state a max value in many datasheets, whereas the max noise of the original 78xx, 200µV, is close to the typical of the 317...), so imo's short statement was wrong. But again ripple rejection was typically 8dB better in the LM317. Ripple noise (often typically harmonics of mains frequency) would be much more annoying in many audio applications compared to a linear reg's own noise, which is more wideband. So the choice would depend on the specific application and of course on the PSRR of the powered circuitry.
I think the LM317 load regulation was also slightly better. So all this was only to be considered maybe 2 decades ago or more.
Either way, for this level of noise to matter, the analog circuit would have to have high gain, and poor PSRR. Otherwise it would not be noticeable.
But yes there are now dozens of alternative regulators for this. The UA78M08 has better specs than the original LM7808, and similar ripple rejection than the LM317, and it's cheap, so it's better overall. It can put out 500mA only, but that would be a good fit in the OP's case.
To get back to what the OP said, they would have to explain what "noisy" means. If it's a matter of ripple noise, then yes ripple rejection would matter, but if it's so noisy as to be noticeable, a few dB better ripple rejection would probably not make a lot of difference. Maybe they could just post the original schematic. I suspect the input (rectified) voltage was very poorly filtered, or something like that. Or maybe the layout is a disaster. Or probably both.