Many people (esp. Dutch people...) go to Antwerp to visit the "Vogelenmarkt" ('bird market'). Don't be fooled: it is a (flea) market as any other and the time when all sorts of birds were on sale is long gone. At present, only a small part of the market is dedicated to pet animals following protests of the animal rights organizations a couple of years ago.
Fun Alternatives: Don't waste your time: don't make the Vogelenmarkt the main focus of your visit to Antwerp. Go and see Antwerp's architecture, its culture, its shops and of course the cafes... and go to the Vogelenmarkt if you have some spare time left.
Leonidas is another famous Belgian chocolate brand. Their shops open towards the street and you see many people line up there to buy some.
Unique Suggestions: Don't! Leonidas pralines are not necessarily handmade and the quality at the shops mentioned in my Shopping Tips is much better.
Fun Alternatives: Go to my shopping tips and buy chocolates in smaller, more exclusive shops like Burie or Godiva.
It will save you a lot of time and the price won't make much difference.
Flandria Boat tour: you can go for a boat trip on the river Scheldt for about an hour, but the harbour isn't that beautiful and my Aussie mates were bored. There are however other trips to places further away that are nicer (like to Vlissingen), but they are daytrips.
A horsecart tour around the Old Town is really not worth its price. Touring the town on foot is a much more genuine way of doing it. Also avoid going for a drink on the central streets of Wapper and Meir - this is where most tourists go, and you're bound to pay too much. Venture out to the nearest side street and enjoy your coffee or beer while discovering new, less known sights.
All diamond museums ... & the nautical museum as well (in The Steen); an outside look is more than enough if you're not a fanatic ...