Erin,
Here's a website that shows all the vegan restaurants in mid-town. Unfortunately you're not in a great area for vegan choices

.
However, you're in luck because you're in NYC, not Podunk. You're sure to find a deli or two near your hotel, and they will likely have bagels and hummus (and I've even seen them offer tofutti cream cheese at some). You should be able to find fruit salad as well.
Now, it looks like there's a Better Burger about 9 blocks away (#1 on the list), which isn't terrible, but I don't know what you consider "walking distance". Anyway, they do deliver, so you might want to check out their menu and make a note of their phone # in case you want them to deliver. We only discovered Better Burger on our last trip there and we ate there 3 times!
That area west of 9th Avenue has tons of ethnic restaurants, so you're sure to find something. Zen Palate (2nd to last on the list) is there too and if I remember correctly, completely vegan.
Here's a list of restaurants in the area and it looks like
The Soup Spot has some choices and is close by. I also see that there's a
Golden Krust bakery with some vegetarian choices. According to SuperVegan the rice and beans and plantains are vegan.
I hope that helps a little. You really shouldn't have any problems. If you get a chance to get uptown, I highly recommend
Candle 79 at 154 E. 79th near Lexington. It's pricey but totally worth it. The first time I went there I took a group of non-vegans (not even vegetarians) and they all loved it.