I'm 5'8" and my inseam was measured in a bike shop as 83.5cm. When I measured myself against a wall and a book, I measured 83.0cm. I was told I could take either a Trek (touring bike) 520 in 51cm or 54cm. The difference is whether you want your arms higher up to be slightly more comfortable over longer distances or whether you want more agility. I'd prefer the 51cm for more maneuvrability.
Charts and sizing calculators recommend 56cm which means if I go 51cm or 52cm, I'm two sizes below 56cm. I'm not the only one here who said they prefered two sizes below. Now, for bikes measured in inches, I find it more difficult to say. I'm really comfortable with 18 inches although I think I'd slightly prefer 17 inches with 16 inches being the one I'd want to feel in total control if I wanted to jump a curb etc.
I don't know what way you want to lean between mountain, road, hybrid, comfort, cruiser etc. But, in my opinion, I think hybrids/touring bikes make a rational choice. I think the GT Traffic 3.0 is an intersting choice (and Kona Smoke).