A couple of points.
First, there is nothing inherently wrong with a hybrid. They serve many useful purposes. There are a couple of significant differences between hybrids and cyclocross bikes:
1. The handlebars (the most obvious difference). Hybrid bikes have flat handlebars, like a mountain bike. Cyclocross bikes have drop handlebars. This means that your primary riding position on a hybrid will have your hands grabbing a horizontal bar, with your elbows poking out to some extent. On a cyclocross bike you will generally ride on the brake hoods (much like bar ends on a mountain bike) or on the drops. In either of these positions your hands will be vertical and your elbows will generally point down, keeping things a little more streamlined. Cross bikes also have narrower handlebars, so they are less likely to catch on something.
2. The geometry (in general). Cyclocross bikes generally have slightly more aggresive geometry than hybrid bikes. This means that they are a little less stable and more responsive. This is mainly a matter of personal preference.
3. The price (almost always). Components for drop handlebars are more expensive than for flat bars. As a result, cyclocross bikes almost always cost more than hybrids. For some people it is worth it. For others it isn't.
One of the lowest cost cyclocross bikes on the market is the Bianchi Volpe http://bianchiusa.com/06_volpe.html
. This has gearing somewhere between a mountain bike and a road bike, so you can take it pretty close to anywhere. It also has mounting points for racks and fenders if you ever choose to add those. I recently picked one of these up and have taken it on a fair number of rides (on road only). It works quite well to tow a trailer with my 9-month old son. I do have to remember to slow down on corners, though.
My suggestion is to pick a few bikes that look good to you and then find somewhere you can test ride them. The best bike for you is not necessarily the best bike for anyone else.
Good luck with your decision and God bless!