The quietest tires I've had were some Dunlop's that,
unfortunately, are no longer available.  I currently have
Toyo T1s. For a performance tire, they have been very good,
but after 8-10 K miles, they became noisy.  On concrete or
blacktop, at 70 MPH they are louder than the dual outlet
muffler I installed!

Randy

The quietest tires I've found have been Avons, the Tech M550 A/S. I don't have
them on the Miata, but do have them on the wife's BMW with sport package, and
they're terrific. Both very, very quiet, and excellent in the wet.

-- Larry

We have Bridgestone Turanza's on a 2002 Miata and you can hear the
radio fine. They cost about AUS $250, which seems a lot for a tyre, but
so far I'm very pleased with their handling (dry and wet). Not sure
about their longevity or whether you can buy these where you are. My
initial reaction to replacing them was it was too much money (they have
a few months left in them so I am planning ahead). I am now thinking
the money is well spent after I tried to get the ABS going at about
75kmh on a wet road and could not get them to lock.

Like you I am was not seeking the best possible performance, but wanted good performance with comfort (ride and noise) in an all season tire.  I decided on the Falken Ziex 512 and got them from DiscountTireDirect for $200 and had them mounted/ballanced locally for about $80.  Mine were 15", the 14" are even less.  Though other on-line retailers seem cheaper once you add in the shipping they are not.  The Ziex's are quieter and stickier (after a 100 mile break in period) than the mismatched tires that I had on the car.  I suspect spending twice as much would get you a even more traction and even perhaps better handeling, but it would probably also loose you the ability to run them at all in the winter months and possibly loose some ride comfort too.  Reviews/Opinions overall rated them well in terms of noise with the Bridgestone G009 probably a slightly better choice for a similar tire that is a bit more money (30%?).  If you are talking 14" I would also consider the BFGoodrich Traction T/A (H Rated, other rating are not necessarily good).  The Traction TA are not available in the correct size for the Miata in 15".  Tirerack sells the last two mentioned.  
Let us know what you end up doing and how it works out.