Just to be clear, you probably mean "wise" and not "The Wise", as they are often referred to, meaning mostly the members of the White Council (Frodo, Tom Bombadil and Sauron have never been in the Council
).
But it is different what you now imagine under the word "wise". From what you wrote, I understand you mean something like "who was the best in wisdom and making good decisions". In this, Gandalf could be mentioned as being very successful, however, I think that's not as true as it seems. Gandalf, as it is shown many times in the books, had the tendency to fail - for example, had Saruman been in his place, he would probably not have overlooked the Ring for 50 years as Gandalf did (the fact that the result was probably ultimately better than if he learned it too early is another thing). Gandalf is also often, and maybe too often, led by "pure luck" (as he himself says). Many times, it is not his own wisdom that accomplishes the goal - it is "chance, as we say in Middle-Earth" - so, the success is not of his doing, but mainly by the power that leads him.
If we speak just of the word "wise", Gandalf himself calls Saruman as being wiser than him, having more knowledge etc. I am sure Saruman was (after all, where would the name "Saruman the Wise" come from) more learned than Gandalf, which of course is the typical "difference between knowledge and wisdom"
But I think at this point, and especially among the Wise (with capital W), the word "wise" means just this: learned. This speaks in favor of Elrond, who has been in Middle-Earth for quite some time and, though for example Galadriel was there longer than him (and she was also at Valinor), Elrond probably is more of the type of "sage", who knew a lot and studied the history, while Galadriel was more into the practical things (like creating Golden Woods, divining from mirrors and learning Khudzul).
Speaking of Tom Bombadil, he was never
meant to be wise - Saruman would probably have the same words for him as he had for Radagast (very similar to what you said about him). Tom is not the one who would care of "big things", as is Treebeard, who, for example, also has knowledge he collected through the years.
So, in conclusion, if Elrond is called the wisest, I won't object. And if you insist that there is also the criterion of "using one's wisdom in choices that ultimately lead to success", then I say Galadriel. She has foreseen things, but (as with the Hebrew prophets, for example), her actions do not rely on merely divining the future, but also - and often more - in correct analysis of the present, and acting on it. Galadriel's results rely on her own wisdom, so all her successes are indeed hers (or at least from the look of it, we don't know to what scale there is "something else at work") - at least in comparison to Gandalf, who is led by "chance" far, far more than her. Now it's not to say, of course, if being led just by one's wisdom is the better way (and as we can see, Gandalf's results were very good), but as an answer to this question, this is it.