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What are your interests? That has something to do with it.
I'd start with installing some free apps. In the music/listening category, I like CBS Radio, Pandora, and Stitcher. CBS Radio features broadcast radio stations and online stations from AOL - there are many, many stations to choose from with all kinds of music and talk. Pandora allows you to enter a song or an artist, and it will play music that is similar. It's a good way to learn about new music. Stitcher allows you to stream podcasts. If you haven't had an iPod before, a podcast is an audio program that you download to your computer, and then sync to your iPod (or iPhone) using iTunes. Although you can stream podcasts to your iPhone using the iTunes Store app, Stitcher makes it much easier to do this.
In the news department, I like the NYTimes, WSJ, and USA Today apps. USA Today isn't the greatest newspaper, but its app is easy to use and has a good interface for weather and sports/scores updates. There are a LOT of news apps out there, and chances are your local paper has one.
I also use location-based services a lot. UrbanSpoon, Yelp, AroundMe, and ManGo are all good apps to find local businesses. UrbanSpoon is solely restaurants, and ManGo is kind of limited to national chains, but all of them are useful for finding a nearby business.