You can use half-clips or even full clips and just no straps. This won't let you pull up on the pedal, but also will make sure your foot doesn't slide forward off of the pedal.

I use SPD pedals and cleats which are "designed" for mountain bikes on my road bikes. The cleats are (mostly) recessed in the shoes so you can walk. In the summer, I use them with Nashbar sandals; when it's cold I just use mountain bike shoes.

My pedals are dual-sided (SPD on one side, platform on another) so I can ride without special shoes if I want to, but I only do when I'm riding my bike in my driveway tuning it up.