There are several specialist food shops around York but for greater choice and a larger selection of products, you might like to go to a larger city such as Leeds (a 20 minute train journey away).
Specialist food shops in York include:
Jojo-s Afro-Caribbean, 45 York Road
Makkah International Foods, 27-29 Hull Road (Halal, Arabic, Turkish and Asian)
Red Chilli, George Hudson Street (Oriental supermarket)
Regency Supermarket, 4 George Hudson Street (Oriental supermarket) Oriental
Express, Hull Road (Chinese, Japanese, Thai and Korean)
Zam Zam, Layerthorpe (Multinational, Halal)