The Ramah in his glosses to the Shulchan Aruch (Yoreh Deah 249:1) rules that the mitzva of tzedakah can only be fulfilled by giving to the poor. This would seem to be the most plausible, perhaps the only, conclusion one can draw from the Torah’s description of this great mitzva.
“If there be among you a needy man, one of thy brethren, in any of your gates, in your land which the Lord your G-d gives to you, do not harden thy heart, nor shut your hand from your needy brother…for the poor shall never cease out of the land; therefore I command you, saying: Open, open your hand to your poor and needy brother in your land” (Devarim 15:7, 11).
Supporting worthy institutions - even Jewish education, as important as that may be - would not seem to fall under the rubric of tzedakah. Tzedakah is about helping the poor, with the highest forms of tzedakah being that which removes people from the ranks of the poor through a loan, or even better, with a job offer. And poor meant poor. The main forms of tzedakah were the kupah and the tamchui, the former being for people who without help would run out of food in a week, and the latter for those who did not even have enough food for two meals.
Money has a tendency to bring out the best and the worst in people and sadly, there are those who would take advantage of public charity funds with false claims of need. They are not deterred by the rabbinic teaching that “whomever has no need to take, yet takes, will not leave this world without being in [actual] need” (Mishna Peah 8:9). Hence we must not take every claim at face value. “Rav Huna says: We check regarding food and we do not check regarding clothes...and Rav Yehuda says: We check regarding clothes but we do not check regarding food” (Bava Batra 9a).
The requirement to judge people favourably does not mean we may act naively. Rav Huna and Rav Yehuda debate where the balance of probabilities of truth and need may lay. Each brings textual support and offers a logical argument explaining why certain claims, but not others, are to be looked into. Rav Huna argues that one who shows up without clothes and asks to be dressed is to be given clothes immediately, no questions asked. The degradation involved in walking around undressed is so great that few are likely to be lying. On the other hand, one who asks for food may have no outward signs of distress and may actually be lying, and thus, his claim must be verified.
Rav Yehuda, whose view we follow, argues that the suffering of a hungry person is much greater than the humiliation of nakedness. Rav Yehuda may agree that one asking for food may have a greater probability of lying; nonetheless, the consequences of a false accusation are much more severe and hence, we give all who request food something to eat immediately. Hunger, the Talmud teaches (Bava Batra 8b), is a fate worse than death.
Interestingly, both Rav Huna and Rav Yehuda quote the same verse to support their claim, highlighting the purposely ambiguous nature of much of the Biblical text (see here where I elaborate on this notion). The Torah allows, encourages, and may even demand that we see various, and at times contradictory, meanings in a text, applying each idea at the appropriate time.
Yet it is not only the recipients of tzedakah who may be cheating. Those in charge of collecting and distributing tzedakah must also be vetted. With so much money at their disposal, the temptation to pocket some is immense. Perhaps counterintuitively – though perhaps not – it is those who least need it who often are the ones most engaged in illegal activity. It is the CEO, not the factory worker, who is more likely to end up in jail. And for good reason. Our Sages note, “the mouse is not the thief, the hole is the thief” (Gittin 45a); the more opportunities people have to cheat, the more they will, regardless of their economic situation.
Our institutions can only be as strong as those who run them. “Rabbi Eliezer ben Yaakov says: one may not give [even] a prutah [penny] to the pocket of [one collecting for] tzedaka unless the one appointed over it is [as trustworthy] as Rav Chaninah ben Tradiyon” (Bava Batra 10b). Rav Chaninah ben Tradiyon is the one who, when being literally burned alive by the Romans, refused to open his mouth so that he could die sooner (Avodah Zara 18a). Before telling us about his martyrdom, the Gemara notes that he once mistakenly gave his personal money which he had set aside for Purim to the poor, and instead of just repaying himself from the charity money as was his right, he also gave that money to the poor.
For those of us in the West, it may be difficult to fulfill the mitzva of tzedaka as originally conceived. Social welfare programs ensure that few need go to bed hungry, walk around without adequate clothing or sleep without a roof over their head. We can thus focus much of our giving on the many other causes most worthy of our support as we fulfill Rav Assi's observation that “the mitzva of tzedakah is equal to all others.”
 Presumably this does not mean fully naked, though it clearly means that one need only look at the clothes to realize he needs help.
 The verse in question (Yishayahu 58:7) is the prophet’s answer to the question asked by the Jewish people regarding why G-d does not respond to their fasting. Yishayahu explains that the purpose of fasting is to sensitize us to the needs – specifically for food and clothing - of those in need. Rav Huna and Rav Yehuda’s argument regarding how to explain which takes precedence is beyond the scope of this devar Torah and not relevant for our purposes. What is relevant is that the Sages choose this chapter as the Haftarah for Yom Kippur morning.
 This is a corollary to the thirteenth and final rule of Biblical interpretation of Rabbi Yishmael, “that two verses that contradict each other until we find a third verse that determines between them.” Not only do verses of the Torah purposely contradict each other, demonstrating the many shades of grey the verses are talking about; often within the same verse we can find opposing meaning, each one correct in its proper time and place.
 Perhaps fearing that some may use this as an excuse not to give charity – after all, how many people do you know who can be compared to Rav Chaninah ben Tradiyon? – the Shulchan Aruch says we can give it to any trustworthy person.