I can think of at least two approaches:

1. Go to the "best" local bike shop (LBS), explain what you're looking for, and ask what they'd recommend. If they want to sell you a $5,000 racing bike, go to the second best LBS and repeat.

2. Play around online. Look at the web sites of Trek, Specialized, Fuji, Giant, Surly, etc., and do an in-depth evaluation of all the models that look interesting.

There's an option 0.5 you should try before either of the above, but most people skip entirely. Figure out what you're looking for. If it's a direct replacement for the original bike, figure out what it had, how it worked, what didn't work, etc., etc. For instance, if it had 700Cx20 tires, did you have issues with bad pavement? Look for a bigger tire next time. Have a hard time with hills? Look for a compact double or triple. Did it have a rack and you used panniers during your commute? You'll want rack mounts on the next bike. If you follow through on this step, you'll have some basis for your evaluations.