I spent lots of time finding how to convert Visio drawing to EPS.
There are many complected ways given. Some of them do not produce good vector images.
Here is the tips for easy conversion.
1. Draw Visio figure.
2. Save as Enhanced Metafile (.emf).
3. Download Free (Open source) Metafile to EPS Converter from http://wiki.lyx.org/Windows/MetafileToEPSConverter and Install.
4. Convert your .emf file.
It works perfectly for me!!