In our search for the best breakfast place in Tel Aviv (as mentioned here) we went to Gilly's this weekend. This restaurant is located in a rather boring looking building (although it has an amazing sea view, being located in the port of Tel Aviv, and a terrace where you can sit by the sea, but we couldn't do that, since it rained this weekend), but is well known for their breakfasts, which you can enjoy until 17.00 every day. It's also located right new to Moul Yam, which is considered the best restaurant for sea food in all of Israel by many, so it's a good place to try to find for that reason alone.
The breakfasts here are pretty expensive (we believe the one below cost 72 shekels, which is way more than most places charge for a breakfast) but they are huge, so you can easily share a breakfast with someone if you want. And you can get a lot of additions to the breakfast (most of them without any extra charge, which is unusual in Tel Aviv), which is nice as well. You also get a champagne cocktail with your breakfast, so if you do like some alcohol with your breakfast (hey, we won't judge!), this is a great place to start your day.
The restaurant itself is charming, although obviously not renovated recently, and the service was excellent.
People we've talked to say that the regular food (meaning not the breakfast) is excellent at Gilly's too, but we haven't had a chance to try that yet. But we will definitely come back for the breakfast, even though we do think Dallal is slightly better than Gilly's when it comes to breakfasts.