CHEF'S TABLE RECOMMENDATIONS IN NYC?
There aren't that many chef's tables in NYC to begin with (real estate wise I guess it makes more sense to just make the kitchen smaller and put more smaller tables in the regular dining area especially since smaller tables can turn faster).
What's your budget, including tax, tips, and drinks? I always associate chef's tables with luxury + long tasting menu so I'm not sure by what you mean as not expensive.
Also 9 is a lot of people, especially if it includes young children (do they have the patience/stamina to do a long meal?), as some places simply can't accommodate parties larger than 8.
The only place I can think of that for sure can do such a large group (9 people) is in Brooklyn: