If you follow the law to the letter once you hop on a bicycle you're not a "pedestrian" anymore and instead are a vehicle. Thus in most areas it's illegal to ride your bike on the sidewalk but in terms of enforcement that's another story. However, in general it's better to ride in the road. You can generally see further, less debris, less tree roots pushing up the sidewalk, not constantly going over the gaps between sidewalk slabs. Plus you don't have to worry about (as much) of actual pedestrians doing crazy things. Look up some threads about MUTs (Multi Use Trails) and you'll see that a lot of people here even refuse to go on those, much less a sidewalk.

Congrats on your new purchase. The Trek FX series is nice esp when you don't like the full tuck of a full road bike. If you ever want more speed though I think you'll end up on a full road bike. I tried the hybrid, but ended up just buying one mtn bike and one road bike instead.