While Blue Bayou is, as Wes said, the place to impress at Disneyland, it may be difficult to get in if you don't have reservations, and reservations can be hard to come by if you don't make them a few weeks (up to two months) in advance. It's also fairly pricey.
If you aren't able to get in there, a nice alternative is the Cafe Orleans, right next door. Even if you experience a wait there, I've never gone more than 20 minutes or so before getting a table. The outside dining provides a sidewalk cafe-like experience perfect for people watching, with a view of the Rivers of America, and you may even luck up on some jazz entertainment from the nearby streetmosphere performers. Or, if you go in the evening, try to plan your meal shortly before Fantasmic starts and stay for the show during dessert. The restaurant offers some of the same menu items as Blue Bayou at a slightly reduced price, if I remember correctly.
Bonus: Both Blue Bayou and Cafe Orleans are just steps away from the largely forgotten Court of Angels, just behind the shops near Pirates of the Caribbean. If you're looking for some alone time in a romantic atmosphere, steal away back there for awhile, perhaps with a couple of cool beverages from the nearby Mint Julep Bar (by the train station). It's my go-to spot at Disneyland for getting away from the crowds. The only other time I've ever seen anyone else back there (including times when the park was filled to capacity), was when a photographer was using it as a backdrop for a couple's engagement photo.
Big Thunder Trail is also good for getting away from the crowds, and though I think the Court of Angels is more picturesque, the dimly-lit Trail does offer its own special atmosphere at night.