In response to Joe's question, it's a wonderful experience at Aikikai Hombu Dojo as one rarely has the opportunity to train under so many high-ranking Senseis at one location. Also, the normal classes at the 3rd level dojo has 90% yudansha. It's a great opportunity to learn from people who have practiced for many years - one might also get lucky when your uke for the session happens to be a 6th or 7th dan
There is also a good article on grading at Hombu Dojo here:
In response to Daniel's questions, from my experience, the reception does accept kyu grading certificates from Aikikai recognized organizations. The beginner's classes are quite basic - as the article above points out, people from 3rd kyu and above tend to attend classes at the 3rd level dojo. Also, there seems to be a jump in difficulty between the beginner's class (the 2nd level dojo) and the normal class. One of the good things about the beginner's classes is that one enjoys more space on the mat... the classes on the 3rd level dojo tend to be packed, so it's nice to have more freedom to move around...
Hope this helps