I have a real soft spot for Malacca, because it was the place my wife and I first dated, so I tend to see it through it rose-coloured glasses. We enjoyed a trishaw ride in the evening and had a candle-lit dinner, and the trishaw driver met us to take us back to our hotel. It was definitely a lot better than an official tour.
This is the historic centre of Malaysia. There are a lot of museums, but there's also a lighter side. The river tour is hilarious, and the locals have a good sense of humour. (It's also a UNESCO site.)
If you're staying for dinner, the Portuguese settlement is the place to be, with lots of local seafood places offering fish caught that day.
A walk up the hill to the site of A'Famosa is a must, because this is where the Portuguese first "discovered" Malaysia, although before that there was a lot of trade within Southeast Asia. I particularly enjoyed seeing the local pictures, and my friend Darren bought one. He was quite taken aback by the very high standard of English of the seller and talked with him for a good 10 minutes.
Quick Tips:
Don't go on a Friday, as the museums have reduced opening hours.
The nightlife in Malacca is pretty limited, so I'd suggest a nice early start; mornings are the best time to wander around the town on foot before the day-trippers come charging in and you feel the heat of the sun.
Best Way To Get Around:
I'd recommend parking your car and walking around the city. By Malaysian standards traffic is slow and there is pavement in most places. There are also trishaws, which are much better than taxis because many of the roads are very narrow and clog up easily.
Negotiate a rate for a trishaw tour. When my wife and I were first dating, I asked for a tour, and he took us nearly everywhere, dropped us off for dinner at a beautiful seafood restaurant by the river, and then picked us up again after we'd finished our meal. These guys really know the city and are very happy to tell you about their town. (One other hint: The older the driver, the better his English tends to be, because the older drivers will have been British-educated.)