"Half the fun of the travel is the aesthetic of lostness." - Ray BradburyMaps. I'm a firm believer in them, especially when you have somewhere to be at a certain time (or if you're trekking through the wilderness-definitely want to know where you're going). But if you are traveling somewhere new, and are unrestricted by time, then I say, toss the map and get a little lost.
Sure, most maps have major attractions marked, popular restaurants, etc. But, let's be honest, sometimes you want to avoid the big stuff and find something really unique to that destination. When you are not reduced to a select group of streets and neighborhoods, you can decide which path to go down, whether to turn right or left at the next corner. This is how you stumble upon that hole in the wall lunch spot, that local artist selling home-made items for a lot less than the products in the tourist traps, or the tiny church that barely takes up a quarter block.
I think some of the best aspects of a location are found off the beaten path, and it's hard to get there if you're following a map that everyone else follows, too.
So step off the designated route and don't be afraid to get lost, because that's when true beauty is seen.