The only other quiet/romantic one I can think of off the top of my head would be Bistro de Paris - which is the upscale one above Chefs in France. They routinely have folks proposing/celebrating anniversaries there, it tends to be more couples than families, and they don't participate in the 180+10 ADR system, so you can only make ressies 30 days out....
It would no doubt fit the bill, but it is located inside Epcot. The OP has stated her family does not have park tickets.
After re-reading your OP, I actually think that GF Cafe might be an excellent fit for what you want. It won't be as expensive as other suggestions like California Grill, Citrico's, etc. It is really nice, and the GF is definitely an impressive place to make people see the "other side" of Disney. Nice and quiet, not in the parks....I think it would be perfect.
I don't think you've said how many people you have, but there are several restaurants that offer private rooms. Mouseweddings.com has a good write up on them (though some can only be booked if you're doing the wedding through Disney, not sure which ones):
http://www.mouseweddings.com/weddingrestaurants.html
Also, have you checked out the Wedding board here at the Disboards? You don't have to be doing a wedding through Disney to participate at this board - everyone's very friendly!
We got married at the Yacht Club this past February and did a dinner at the Sonoma room at California Grill. We had to do a minimum of $2000, and with the smallest dinner price being $80 it was easy to meet that. But it was a lovely room, we private servers and then we went out on the deck and watched Wishes right before the main course. It really was amazing and even those who weren't very "Disney" really enjoyed it.
Good luck!
ZoZo -- Not sure what night you were at CG. Every time we've been there, it's been insane with tons of noisy kids all over the place.
I thought California Grill (at the Contemporary) was nice and quiet. The tables aren't squished together, and the atmosphere is rather elegant. Since it's an upscale, more expensive restaurant, you don't see families with lots of little kids (hence, noise). If you get a later reservation time (8:30 or 9:00 pm), you'll have a better chance of having a nice, quiet meal.
(And the food's great, as well!)
Having been to all the signature restaurants numerous times, I can say with certainty there is not one that is relatively quiet. Artist Pointe and Jiko would be the best of the bunch.