Currently have a C corp and trying to become more tax efficient. Thinking about converting it to an S Corp. However, I want to keep the EIN the same. What's the best way of going about this?

yes you can; but if you want, you can get a new EIN no problem; When you convert an c(or s)-Corp to a s(C)-Corp, you are changing the tax status of the corp. The base corp is not changing (same legal entity) and also the ein of the corp is also not changing. its like getting married, name can change but social security number does not.