The wine culture in Israel is still developing. More people get exposed to the idea of drinking wine as a casual daily act. One thing that helps it develop is the strong local wine industry. The Israeli wines receive recognition and high rates by wine critics from all over the world (Robert Parker, maybe the most famous one, includes Israeli wines in his magazine since 2007).
There are many places in Tel Aviv where you can purchase local wine. My favorite place is Gary’s, which is the informal name for the medium-sized store, located on Arlozorov-Ibn Gabirol junction (according to the website, the name is Wine Selection, but no one uses it).
In the store you’ll find a large variety of wines, local and from abroad, at a wide range of prices. I prefer to buy at Gary’s since he has good prices (it’s not half-price, but usually it’s going to be the lowest price you can buy this wine at) and because if you don’t ask for help, no seller will push himself into your wine search. It doesn’t mean you can’t ask the staff for help, they are really nice; they just respect your privacy.
P.S I just found out they are doing deliveries for 25 ILS.