Luang Prabang has its own 'royal' version of Lao cuisine. Unfortunately, few of the many restaurants catering to tourists offer much of it. Which is not to say you can't get good eats around town. The city is quite full of places to eat, with everything on offer from European to Thai to Lao cuisines, and we can honestly say that we didn't have a bad, or even mediocre, meal there.
The small cafes along Sisavang Vong Road are good places to catch a snack and a cup of coffee at any time of day. The French roasted Lao coffee is always good. Several bakeries offer delicious sweet or savory rolls and pastries.
Aside from the restaurants along the main road, there are several waterfront restaurants along the Mekong river. These are mostly only open at night.
Restaurants and cafes seem to come and go. At least a third of the places listed in the current big name guides are gone, or changed hands, so we won't bother trying to list them here. Just wander around and see what looks good, and check out the most recent reviews of Luang Prabang restaurants at my travel journal.