The context is about lodging, so I would be tempted to say that this is not the “praise” sense, but rather the “rent” sense. However, “se louer de” is simply not sensical in this sentence no matter which sense you’re going for.

I can’t find mentions of the construction for the sense “rent” (louer² tab), and with the “praise” sense, it means “congratulate yourself for [something]”, and it just doesn’t seem to fit the syntax or the overall meaning here.

If we speculate that this is actually some sort of a slip of the pen, the dual senses of louer still make it impossible for us to tell whether he’s always enthusiastically recommended this boarding house, or if he’s merely saying Dumas never failed to find an available room there (e.g. if the pronoun is où and not dont).

J’ai toujours eu à me louer de…

has the same meaning as:

Je n’ai [jamais] eu qu’à me louer de…

Here, the A la Croix de Jeannette clothing shop is simply recommended / praised by Dumas.