Then again, if everyone had acted "wise" -- recalling and acting on all possible available knowledge and the most opportune moments, which is the implication I'm getting of the definition, here -- there wouldn't have been much of a story. I do agree that there is a strange inconsistency with the Elves' and Dwarves' apparent knowledge of the presence of a Balrog in Moria, and their lack of action to get rid of it. Personally, I think that Gandalf knew it was there, but hoped that it had buried itself so deeply in the mines and was dormant for so long, they might have a chance of getting through if not unnoticed then before it had a chance to awaken and come up out of its hiding place to get them. He would have reason to believe it possible, since he had been in Moria before, with Narya, and had gotten out again without (apparently) even stirring the creature's attention. He knew that the Ring drew evil things to it, and thus would probably have known that they had to make it through as quickly as possible. And if they didn't make it, he was obviously prepared to sacrifice himself for the quest.
When Legolas cries out "A Balrog!", Gandalf's response is, "Now I understand." But he never says precisely what it is he understands. That the evil thing with the orcs is a Balrog? Or that Aragorn's presentiments of danger and doom meant that he would die in this particular way? Or something else entirely? We're never told, although we do know that Gandalf was aware that he might not make it through Moria. As Aragorn later told Gimli, "The counsel of Gandalf was not founded on foreknowledge of safety for himself or for others," a sentiment which is echoed in Galadriel's reproach of Celeborn, "Needless were none of the deeds of Gandalf in life. Those that followed him knew not his mind and cannot report his full purpose." All these things tend to make me think that Gandalf knew that there was a Balrog in Moria, and that he would face his greatest test (after the Ring) there: to lay down his life for the sake of his mission to Middle-earth, and thus personally fail to see that cause through to the end. "Now I understand" may have referred to his choice: to merely help the Fellowship out of Moria and go with them, letting others deal with the Balrog (which no doubt would have resulted in greater destruction and death in Lothlorien, and perhaps elsewhere), or facing it himself and very likely dying (since no other being in a true body had ever taken out a Balrog without perishing in the process).
In my experience, wise people generally don't go around advertising the fact. Which makes one wonder about "Saruman the Wise," who apparently liked being called that. At least it makes
me wonder.
Cirdan, however, seems to have demonstrated the age-old wisdom of discretion being the better part of valor.