Accurate turning without encoders

OP, you can try the 4 distance sensor idea, however, all of these schemes will be off by a few degrees
at the very least. Sonars have wide beams, even the "narrow" beam ones like Maxsonar EZ4, and Sharp
IR rangers have a limited distance range and poor accuracy at longer distances. OTOH, even encoders
won't always work well, due to wheel slippage,etc, on different surfaces [carpet vs hard floor], or where
the 2 wheels are each on a different surface.

You might try a 2-stage scheme, of first turning at a set speed for a specific time-period [determined
experimentally], and which will by off by 10-20 degrees in general [I've tried this], and then adjusting
the angle using one of the sensor schemes.