I live a few blocks from Serendipity and Dylan's Candy Bar...I avoid East 60th Street like the plague once it gets warm out because the lines of tourists standing outside is ridiculous. Don't waste your time waiting for a frozen hot chocolate. The store is cute, but cramped and completely un-authentic to any "New York" experience. It's nothing but little kids and tourists.
Unique Suggestions: Don't block the entire sidewalk while you're standing around endlessly waiting to get inside. It's obnoxious to the people who are trying to get by.
Fun Alternatives: If you're looking for great desserts, try Cafe Lalo on the Upper West Side instead.
I used to go to Serendipity's all the time as a child. Then it became a tourist trap. Only tourists go there, like the Statue of Liberty. It's charm has been completely washed away with the drab masses of white sneakers and scrunchies harassing midtown East. Now it's crowded, takes 3 hours to get a table in high hours, and the food just isn't that great anymore. The staff is overworked and tired and just want to leave. And it's loud, the children are rude and obnoxious and it's such a painful experience to go. I wouldn't recommend it at all.
Unique Suggestions: Get the frozen hot chocolate and or the humble pie.
Fun Alternatives: Want to treat your children to sweets but want something classier than Serendipity's, where all the tourists go to recreate movie moments? Go to Charbonnel et Walker, 8th Floor of Saks Fifth Avenue (see my Shopping Tip). It's a beautiful little chocolate shop that is simply a fantasy to enter and far more beautiful and classy than Serendipity. Far better experience than being jostled by other tourists