By far one of my favourite Parisian areas - you feel like you've been taken back to the '40s with the traditional paintings, people playing accordions, cobblestone streets, great little restaurants (recommend Le Poulbot in one of the side streets), and fantastic views of Paris. We sat on the steps of the Sacre Coeur and watched a bit of street theatre after our meal as Paris glistened in the sun below us.
Sacre Coeur itself is worth climbing up, as the views from the top are fab. I usually do any tourist shopping here, as it's the most fun place to do it, maybe not the cheapest, but definitely the best experience.
The square in the centre is full of painters, and you just can't help walking around to look at all the art or taking some photos (although many make a point of asking you not to--oops). In the evening, why not sit in one of the restaurants as you watch the world go by in these artistic surroundings. If you have some extra time, go towards the back of Montmartre and explore the vineyards. You wouldn't expect any in central Paris, would you!?