I'm moving to NYC: advice on where to live

[dogdrool]

I just took a job on Wall St (well, the office is in Times Sq), and I would love any advice on where I should live. I have (small) dogs, and I don't want roommates. I'm expecting to spend between 2500 and 3000 per month for a decent place. (I'm looking to rent for a year or so while I get used to the city)

Can anybody tell me:

1) how realistic my expectations are in term of cost?

2) what neighborhoods I should focus on?

I want an easy subway ride, or walk, to Times Sq. It's also very important that I'm near a place that I can let the dogs run off leash. Also, I want something larger than a studio.

Finally, slightly off topic, can somebody recommend the absolute best dog walking service or dog daycare service in NYC?