Salvation Army is one of the better National organizations to donate money to also for every dollar donated they give $0.98 to the programs and only $0.02 to admin costs, pretty good ratio if you ask me.
Not knock any local organizations if you have a local one that you like the work they do give to them, always great to give to a quality organization.
When we lived in a smaller town (2000 population.) dad was the preacher at the local Christian Church he and the rest of ministers got tired of lowlifes making the rounds and collecting from every church in town. The churches got together with the police and formed away to weed out any fraud, they had accounts at all the local businesses (gas station, grocery store, five and dime) every minister could write a voucher for anything available catch was you had to stop by the police station and get it signed by cop on duty before it was good, kept the local community chest fuller and more available to give when a local tragedy struck. After we moved to a larger town that had organizations in place dad cleared out the food pantry and cloths chest at his new church and explained to the church board that instead of having money sitting in an account for the minister to give hand outs that it would be much better giving more to the local charities that are better equip to deal with fraud and have way more services available for those in need. So when someone called dad or the church they sent them to Interserve (local food bank) or the Salvation Army. I remember some of the food in the Church's food pantry was over a decade old that was not something I would want, I would eat it if i was hungry, but it would make me feel a little more like the dregs of society than I would have felt already. I've strayed from the topic a little of clothes donation but I wanted to share why I commented as I have today and in the past, as well as how I come by my knowledge on the subject.
I'm personally not big on the Red Cross, not that they don't do good work just too high on the admin ratio and for some of their past deeds, ask a WWII vet about the Red Cross I'll bet you get an ear full. Things like selling cigarettes donated by tobacco companies for the troops to the troops.