I've never been to the WH either but I've been to the Mall and some of the memorials. Viet Nam memorial had special meaning for me. They don't charge admission, they all belong to us.
I've been there twice. There is no charge, but you have to get the tickets through your congressman. First time I went through Nixon was president. Got my ticket from John B. Anderson who would run for president as an independent in 1980. Still got the letter but I'm not sure I could find it if I had to...