There are many markets at which to pick up some native Azerbaijani cuisine in Baku, just make sure you check expiration dates—the occurrence of vendors selling expired food products is more of a problem in smaller shops than in more upscale supermarkets.  

Although bazaars and markets are open throughout the entire year, fruit and vegetable options get a major boost come summer.  Major markets worth checking out include: Citimart, Continental, New World x 2, Lider, Sevimildad any of the five Ramstore Supermarkets. Bread from local Corac shops is great.

Bring your own clothes—local apparel stores vary too much in selection and quality.  (Western women arriving in the area do not, however, have to worry about changing their garb as few Muslim women in Baku wear chadras.)

There is one English bookstore in Baku - Chiraq Bookstore.  They are a good place to go for travel guides, dictionaries, novels, books about the history and culture of this area, and  kid's books.

Baku is known for its carpet-makers, and their product make for great gifts, souvenirs, and mementos, not to mention art.  Most Carpet seller's can be found in the old city, you will have to haggle to get a good price.

The old city is worth a wander around, with many old buildings to see.

Do not drink the local water, bottled water is a must.
For full Baku shopping info, go here .