It'll really depend on your city. There's literally THOUSANDS of geocaches in every city, so it could be in your neighbourhood, downtown, or a local park.
just go to the geocache website and choose the ones near where you are. Read the descriptions and see whether you'll need to traverse through any woody areas to get to the geocache.
My friend and I went geochaching a few months back and we started at our college, went to the train station, then by two housing communities, a park, and finally downtown.
We had to crawl through quite a bit, since many of them were hidden in bushes and trees, so you may just get dirty!
It's really fun though, since geocaching gets you to explore many parts of your city that you've never seen before! Good luck and have fun!
Ah, I almost forgot! If you have an Iphone or Ipod, there's a free geocaching app that'll tell you your nearest geocache. It'll tell you the area, but won't show you where it is exactly (that'll ruin the fun of it)
Just search for "Geocaching" in the App store, and pick the free one!