The motivation for shipping Aemon to Oldtown felt like bullshit to me when I first read it, and after slogging through all the Samwell chapters, it still feels like bullshit.
Martin needed a reason to tell us about the dragons and archmaesters, why couldn't it just have been Samwell delivering a message to the archmaesters from Aemon -- and absconding with Gilly and the king's blood-ed baby while he's at it? That would have worked equally well, I think.
Jon/Aemon's decision to send a 102 year old man on a sea journey just seems completely stupid. On the Wall, so what if Aemon might be threatened by Melisandre, it's still uncertain if those conditions on the Wall will lead to his end. A sea voyage, OTOH, is certain death for Aemon, how can you expect a man that old to survive that? From the very beginning, I expected every Samwell chapter to somehow announce Aemon's death.
There's a few points where I think Martin forces things unnaturally, and that's one of them.