For outdoor activities, the most exiting place is probably the Zapari bird park. Kids love it and you can spend a whole day there. Here is the link: zapari.co.il/?categoryId=352... All these area is a made of several parks, linked to each other, and towards South West, in one of the parks, there is a small zoo for kids your age. Further to West, you can rent a pedal boat on the Yarkon river. Not far away from it there is the Meimadion water park, but I think that this one opens in only in June (I don't know when you plan of coming here): meymadion.co.il/?categoryId=... For the weekend, you might consider Tel-Aviv Luna Park, though I don't know how much a 4 year old kid will enjoy it: lunapark.co.il/?categoryId=2... A slightly different type of activity you can find in some shopping malls, such as Gan Ha-Yir (near Tel-Aviv municipality, entrance Ibn-Givirol 71). This one has a large, well-equipped playing area for small kids, named Ba-La-Gan (a double meening pun in Hebrew, meaning both come-to-the-kindergarten and big-mess). Kids can play hours there while you can do some shopping; just be warned that Gan Ha-Yir is one of the more expensive shopping areas in Tel-Aviv.
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