I highly, highly recommend Alicia's place on the Bowery, right next to both Chinatown and Little Italy.
We (two of us) stayed there with two young children and were pleasantly surprised to find everything we ever could have needed (super comfortable beds, wonderful noise machines in each bedroom, coffee maker, well-equipped kitchen, washer/dryer, reliable internet, apple tv, a luxurious shower--even kids' cups and water bottles to go); nevertheless, it is a stylish, well-done space, perfect for the downtime one inevitably needs after pounding the NYC pavement.
You should know that there are 4 flights of stairs to contend with, but they are doable. Our kids took the challenge beautifully and it offset all of the eating we did at the ridiculous number of wonderful restaurants within a 30 min walking radius (Oiji, Momofuku's Noodle and Milk Bars, Superiority Burger, Pasquale Jones).
And, Alicia was a great host- with recommendations as needed and just the right amount of communication. Check in and out was remarkably easy.
In short, it's a really great find. Would stay there again without reservation.