I've commuted in NYC for 15 years and only had one bike stolen - a Benotto which I just re-painted with all new decals and some sod must have followed me home and took it right out of my apartment hallway- leaving all my other more valuable bikes alone but I guess bling is popular. Touch wood, my old Centurion Ironman with a hodge podge of de-branded components has never been touched - and the (DT swiss) wheels are quick release which I can never be bothered to lock anymore.
I have a theory that large bikes (mine is 58cm) are not theft targets in NY as they do not make popular delivery bikes but maybe I've just been lucky. So I think your Trek is perfect - a bit beater, huge frame but rides well.