I just stayed at the Hanoi 3B Homestay in Ba Dinh (just north of the Old Quarter and within walking distance of Truc Bach Lake) - it was wonderful, and they do have apartments available. Prices are excellent, they serve a buffet breakfast for their guests, and they treated me very very well (I stayed there 25 days on the hotel plan). I would contact them at booking@hanoi3bhomestay. This location is great, and even on the #14 bus line.