Greetings from the Big Apple!
Re bikes- for most of Manhattan I'd advise against- although you can hire bikes and cycle around the perimeter- if you have time- the island is 14 miles long.
If you like real Asian Food just poke around Chinatown, re rustic type grub.. it really depends on what your taste is (eg there are more French restaurants in the five boroughs than there are in Paris).. for a super brunch try
Capsouto-Freres in TriBeCa.
For stuff to do check out NFT.
If you want some advice re ahem..afterdark activities, PM me, enjoy the rich tapestry of the most dynamic city on the planet- yeah baby!:)