Wow, thanks to all for the recommendations. Moomah is not what I had in mind, but it sounds like a great tip. I have never hit Cafe Fledermaus at the right time . Amy's Bread, Edgars, and the Dutch all sound like great options. Maybe tomorrow I'll give Dessert Truck Works a shot. I find predicting foot traffic difficult this time of year.
I am looking for a place where I can sit and write for about an hour in the afternoon while enjoying a really delicious slice of cake. I don't manage to go out for cake very often. (Like, I have not done it in about three years. Not coincidentally, I have a three year old.) Sadly, my old cake-eating standbys are gone (I assume for the obvious reason that a business based on cake and people sitting around is not likely to pay the rent for long). I think the place I used to go on Greenwich Ave was called Cafe della Artista or some such. It was amazing.
Just to be clear: I am looking for a slice of cake, not a whole cake. I am not, however, necessarily looking for the best slice of cake in New York, as (for example) Cafe Sabarsky has a tasty Sachertorte, but good luck hanging out there, or Silver Moon bakery sells yummy cakes, but I am not looking to take the cake home (see "three year old" above), I just want to sit down and eat a slice of cake, drink a cup of coffee and think for a bit.
I like chocolate cake, but really I like most cake. I also like most places that serve cake. I am happy to go to a diner provided the cake is highly recommended, but I don't have the wherewithal to test out diners. Although --that would be awesome. Chowhound really should have a whole board dedicated to the brave souls willing to try out every cake in every diner in town so that the rest of us might not be forced to eat stale cake.
Reading over, it is clear to me that my prose is not what it could be were I able to eat some cake. But thanks in advance for your help.
Bagels -- you want the place on Broadway just south of 108 (on east side of the street).
Dinner -- depends on the kind of dinner. AWASH on Amsterdam and I think 107 has good Ethiopian. Thai Market is across the street and not bad. I like Sezz Midi on Amsterdam and 122. Toast is fine for BBQ, and the place on the south side of 110 near the corner with Amsterdam has great southern food. For Italian, you need to go a little farther afield. -- several places in the 80's and 90's -- Genaros and Celeste are justifiably popular, but I like Acqua at Amsterdam and 95 because it tends to be less crowded. Turquaz and Mughal Palace are good if slightly pricey places for Turkish/Indian respectively -- they are on opposite sides of Broadway at 100.
As for the strip in front of Columbia on Broadway, I'd avoid it if you really care about food. I do stop into Cafe Swish in the summer for iced coffee and bubble tea.
Can't help with Little Italy.