My first piece of advice is that you should call "Avenue of the Americas" 6th Avenue, or people will think you're a tourist ;-)
Hah! That's funny. Good to know. The address is 100 Avenue of the Americas. (I'll edit out the exact address later.)
Short commute is important.
We are OK with a smallish apartment -- we have room to spare in our 800 sq ft apartment now. It matters more how the space is used than the actual square feet. I'm even up for living in one of those duplex kinda places where the bedroom is up top. My 6'4" husband is hoping we can squeeze our king size bed in, even if we can't really walk around the bed :)
I'd really, really like to have a terrace or deck or yard where we can let the dogs out. This is probably going to be the hardest thing to find.
Nightlife doesn't matter much. We like trying new restaurants occasionally, going to museums, going on walks in parks, and going to Meetup groups in stuff that we're interested in. None of that really requires being in a super hip part of town, as long as it's not really isolated.
Quality of the neighborhood... hmm... not sure how to speak to this. I want to feel comfortable walking around at night? I don't want to feel trapped in the apartment at night.
With cost, I'm more about getting good value of the space. Getting inexpensive housing can make a big difference with saving FI, but I really want to like where we live too so if I can't find a good fit I'd explore my options with a bigger budget. Salary will be ~$125k base until I get a job, as a reference point.
Thanks for your help!