For food , it's easy to find small grocery stores: in the Old City, Souq Khan al-Zeit is full of them, and there are several along al-Wad Road too. Mahane Yehuda market is also a good place.
Israeli and Palestinian wines vary from downright awful to highly palatable, but few are good value. Among the names worth checking out are the Latrun monastery's Cabernet Sauvignon, while others include Golan Cabernet Blanc (a white wine that looks like a rosé), and Barkan and Carmel Select. Israeli beer rates pretty badly, but Palestinian Taybeh is an excellent German-style lager made with all-natural ingredients. Israel also now produces a decent cider called Slingshot. Locally distilled spirits are generally best avoided, but Ramallah in the West Bank produces the country's best araq, an aniseed drink similar to Turkish raki or Greek ouzo; Arak Extra Fine, with a green and gold label, is the best brand. In general, Taybeh beer is increasingly available (though still not easy to get hold of) in West Jerusalem, but Latrun wines and good Palestinian araq are almost impossible to find west of the Green Line.
All Spice Paradise
71 Souq Khan al-Zeit, Old City, by Hashimi Hostel. Daily 9.30am-5pm.
A good place to stock up on sumak, za'atar and other Palestinian spices that you won't get at home (though ones you can buy there will probably be cheaper than here). Ground cardamom seed might be worth buying if you've developed a taste for it in Turkish coffee. The local version of saffron is cheap, but it's very low grade.
Avi Ben
22 Rivlin. Sun-Thurs 9am-8pm, Fri 8am-3.30pm.
An upmarket wine merchant with a good selection of Israeli and imported varieties, plus a small range of beers, some spirits (especially vodka), and Slingshot cider. Also in stock are expensive local olive oils and some interesting cheeses, and this is the most likely place to find any new microbrewery beers.
Barkan
1 Agron. Sun-Thurs 8.30am-11pm, Fri 8.30am-3pm.
This rather refined store specializes in Israeli wines, of which it has a fine selection, and also stocks a good range of vodka and tequila, plus Taybeh and imported beers, and some high-quality Israeli olive oils.
HaMashbir
20 King George St. Sun-Thurs 9am-8pm, Fri 9am-2.30pm.
A pretty bog-standard department store, neither very large nor very exciting, with a limited selection and little that wouldn't be cheaper elsewhere or at home. It does, however, have a reasonable range of perfumes and clothes, and a food section that's as good as any supermarket.
Old City Grocery Store
35 Latin Patriarchate St, by the Jaffa Gate. Mon-Sat 9am-5pm.
A good place for monastery-produced wines (such as Latrun and Cremisan), Taybeh beer, and Ramallah araq. If it's closed, the liquor store just up the street on the opposite side stays open later though it doesn't have quite such a good selection.
Sha'ar David
4 King David St. Daily 24hr.
A run-of-the-mill corner shop, noteworthy only for its opening hours, which make it especially handy on Shabbat.
Supersol
1 Agron. Round the clock Tues 7am-Fri 2pm, Sun & Mon 7am-midnight.
A well-stocked supermarket keeping convenient hours (bar Shabbat), and well stocked with fruit, drinks, confectionery and delicatessen.