The Duck Tour can be lots of fun, especially if the weather is nice. If the weather is awful, the Aquarium and Quincy Market are good choices.

If the weather cooperates, a particularly good way to spend a day or half-day is to explore the Beacon Hill/Public Gardens area. Start at the corner of Arlington and Boylston Streets (about 4 blocks from the Copley Sq. area), and walk through the Public Gardens – it's one of the most pleasant city parks that you'll find in the U.S. When you reach Charles St. (which divides the Public gardens from the Boston Common), turn left, where you'll get a great view of the houses along Beacon Street (it's especially nice early in the morning, when the sun plays directly on the buildings). After you cross Beacon, Charles St is a wonderful neighborhood shopping area where you can refresh yourself with a coffee. Continue along Charles for a block or two and turn right onto Mount Vernon St, which is one of the most delightful streets you could hope to find. This street needs to be walked, not driven. Every building is a treat, and the side streets (of which Louisburg Square is the best example) are amazing. Explore to your heart's content – I like to walk up to Walnut St, then back down Chestnut. When you're tired, head on over to the Common to a bench and do some serious people-watching, or back down to Charles St. for more refreshment.