those boots are made for walking...
 

My first purchase in New York must be a good pair of warm boots for walking the streets in January. Any suggestions of the best place to head for (open on Sundays if possible)...thanks

All the stores will be open on Sundays. Some don't open til 10 or 11 in January. (Now, pre-holiday, they all open around 9 or earlier).

Depends on your budget and what kind of boots you want.

DSW in Union Square is a discount shoe store. http://dsw.com/

All the dept stores have shoes/boots and sales have started! Macy's and Bloomingdales offer visitors an 11% discount if you register at the customer service desk before shopping.
macys.com
bloomingdales.com

The discount stores like Century 21, Daffy's, Loehmann's have boots. For a specialty store with warm, water proof boots, Harry's on the upper west side is good. http://www.harrys-shoes.com/shop/home.aspx

Thank you mclaurie for that very detailed reply. Just what I needed.

Don't you think you should break them in first? I can't imagine walking all day, on city streets, in a brand new pair of shoes.

I would not recommend Loehmanns or Daffys or Century 21 for boots because the selection there are rather hit or miss. And service is almost non-existent in those discount places. I would, instead, head straight for either Harry's, mentioned above, or Tip Top; both of which are on the Upper West Side and are, in my opinion, among the best shoe stores in the city for selection and service. You also might consider ordering boots by mail from either of these places before your trip:

www.tiptopshoes.com

Thanks all. I know I should break them in, but that won't be possible so I will have plenty of bandaids and will always be a cab ride from the hotel if necessary. I can't imagine buying shoes mail order, so I will manage with the great tips I received.