Living in Tel Aviv, your apartment is probably not very big unless you got very lucky. Odds are you don't have a garden but then again - life in Tel Aviv takes place outside. And as you have noticed - Tel Avivians love dogs. If you do too but you can't adopt a dog, you can still foster a dog for a certain period or come to one of the animal shelters and help us walk the dogs there.
I personally go regularly to the Lod Animal Shelter https://www.facebook.com/lod.dogs and it's a great way to meet engaged, activate Israelis - as well as adorable dogs
Message me if you would like to join us