Lunch near Sixth Ave and Canal St?
Bubby's is to be avoided on weekends (it's a creche) but on weekdays it's quiet and their food is solid.
Slightly out of your range but there's a $25 prix-fixe lunch at Kittichai, where the food is very good but service spotty.
If you're staying around that area in the evening then La Sirene is similar to Cercle Rouge, slightly more expensive, but with the advantage of being a BYOB.
Bubby's Pie Co.
120 Hudson St, New York, NY 10013
60 Thompson St, New York, NY 10012
241 W. Broadway, New York, NY 10013
558 Broome Street, New York, NY 10013
I was just there staying at the Hilton Garden Inn at 6th and Canal- I ate at a soup/ sandwich place called Columbine, and it was delicious! They have 3 different soup specials everyday, plus a handful of homemade sandwiches, salads, and sides. The store itself has moved into the space next door with a sign that says "Clementine " on it, not sure what that's about.
Columbine- 229 W, Broadway, New York, NY 10013
227 W Broadway, New York, NY 10013
229 W Broadway, New York, NY 10013
It's at the top of your price range, but Aurora is nearby at 510 Broome. It's lovely and has very good food. They have nice sandwiches at lunch for under 10 dollars, the burger is something like 12 and the pastas are in the 15-17 range.
510 Broome Street, New York, NY 10013
Mooncake on Watts St. Good soups, salads, and I dig their whitefish sandwich.
Sunrise Mart on Broome - nice Japanese selection, market with seating area. Sushi/sashimi, wraps, salads, and made to order udon/ramen soups.
494 Broome St, New York, NY 10013
28 Watts St, New York, NY 10013