I would like to find a martial arts class for a complete beginner
(adult), that starts after 5.30pm (weekdays), in New York City,
preferably in mid-town, west of 5th Ave. Not yoga, not self-defense.

I searched on Yahoo! (
http://dir.yahoo.com/Regional/U_S__States/New_York/Cities/New_York/Business_and_Shopping/Shopping_and_Services/Sports/Martial_Arts/Instruction/
) and Google Directory (
http://directory.google.com/Top/Sports/Martial_Arts/Schools_and_Instruction/North_America/United_States/New_York/
), and found two schools that seem to meet your requirements:

Chau's Martial Arts Center
http://www.chausmartialarts.com/

The New York School of T'ai Chi Chuan
http://www.taichichuan.org/

I also found a third school that appears to meet your requirements
except for location:

Chinese Hawaiian Kenpo Academy
http://www.chka.org/

(While the web sites indicate that T'ai Chi and Kenpo have
self-defense aspects, my sense is that the classes are not taught for
the sole specific purpose of self-defense.)

If you are not satisfied with these options, you might browse the
martial arts schools listed on Citysearch; approximately 100 are
located in Manhattan:

"Sports & Recreation: Martial Arts Instruction"
Citysearch [New York]
http://newyork.citysearch.com/search/?sorted=rank-desc&dlink=1&type=dgrid&context=directory&histo_name=Martial%20Arts%20Instruction&cats=323&c_id=150&start=101

- justaskscott-ga


Search terms used on Yahoo! and Google Directory:

"martial arts" "new york"

Try going to www.mma.tv
On the left they have a "find a school" option.  Give that a go.

Generally on this web-site they're into decent marital arts instead of
the pansy nonsense you seem to want to avoid.

Without knowing New York at all, I'd suggest the Renzo Grazie Academy
at 301 West 37th Street, 5th Floor (Phone: 212.279.6724).  That might
be miles away from you, but given the Gracie heritage (pretty decent
competitors in Ultimate Fighting competitions) it might be worth the
trip.

Otherwise, I personally would recommend anything reality based like
Brazilian Jiujitsu or Shootfighting to be well worth the extra time
spent getting there.

Agree with wilbur111-ga!!!