Every city playgroup rummage sale, we donate our leftover baby goods to a foundation that cares for the needy, mainly the elderly. The foundation has second-hand stores around Taiwan, and the money they raise from selling the donated products is used to help them in their work - giving food, home visits, doing housework, arranging medical care, etc. They take all kinds of things, household goods, furniture, etc and distribute them to their stores.
Their contact information:
Taipei City Sao Shing Bei Street (Jie) No. 23, 2F (near BeiPing/Chungshaio East Roads)
Tel: (02) 2391-8083
You can arrange for the organization to pick up the goods if you have no transport.
(They usually have difficulty finding someone with good English-language skills so it's best to have a Chinese-speaker call.)