If you don't want to do lycra you can always get bike short liners that will fit (well sometimes) under 'regular' shorts or capris. You can get them at REI or anywhere that sells Pearl Izumi stuff. After riding for a couple of years, I don't wear padded shorts all the time, only when I mountain bike where it's really rocky.

The thing where people are saying your feet should be flat is the standover height, where your butt is off the seat, how you would be standing at a stop sign. Your feet should be flat on the floor and you should be able to stand comfortably over the tube of the bike without having to tilt to one side to compensate for the bike being too tall. Hope that makes sense!