$p > 2$ and ramification of archimedean places

Question

Fix a rational prime $p$. I know that for a $p$-extension (ie. a Galois extension of degree a power of $p$) of an algebraic number field $k$, some places can not ramify:

1. complex places cannot ramify.
2. real places cannot ramify if $p\neq 2$.

This is presumably easy to solve but if we assume $p > 2$, archimedean places cannot ramify. Let $S$ be a finite set of places of $k$. Can we assume $S$ to contain those archimedean places and does this alter the maximal $p$-extension that is unramified outside $S$?

Thanks! :-)