This gets asked periodically. Here's my suggestions based on experience:
First off, Wounded Warrior DOES NOT NEED MONEY. They don't help disabled vets. Unless bike rides and bungee jumps are the help you wanna subsidize, plus much of their money goes to advertisements and most of their "events" are donated in some fashion, so I have no idea where all that money went. Sure, they show a few guys on ventilators and get involved in a few things, but it's not their forte.
AMERICAN LEGION --they are who thanklessly pour over and submit and file and fuck with your papers you have to send VA. You NEED them, dealing with VA is a full time job and you need help. Many of their facilities are closing and they could use the help.
AMVETS --I pull for the Legion because that's who I go to but AMVETS does the exact same thing.
If you REALLY wanna help soldiers and their families when they are in the worst part, FISCHER HOUSE. They do things that are beyond the scope of even the VA or any other service. IMO, Fischer House ought to be govt. funded (properly). But it's not, so donations help.
Those guys won't blow money on advertisements and they don't get paid. They do a thankless service for vets though and we couldn't get by without them.