Say I've got a piece of code. Nothing wrong with it; I'm just curious if it's the best way to go about doing what I'm trying to accomplish.
Would those kinds of questions go here, SO or do they not belong on either site?
No. Stack Exchange sites are for specific questions that can be answered. Not code reviews.
"Look over my code" questions do not belong on either Stack Overflow or Programmers.stackexchange.
Since this question was originally asked there is now somewhere to ask this sort of question:
Specific questions with short code snippets are, AFAICT, acceptable on SO. Those questions tend not to be suitable for Programmers.se, since they're not usually subjective. Neither site is for code reviews.
I would like to see a SE that allows this, the issue of course is it would need to be moderated extremely well but it would be nice to have a place were you could get some form of per review.
Most of the questions that involve "code it better" type scenarios are actually based on the fact that a person is stuck trying to figure out good implementation. There are many resources to tell people how to use x, y , z language but there are few and far between that discuss implementation of features.
Having said that if you know the implementations you want to use but are unsure what the pros and cons are of each I find SO is fine as long as you are honest in the fact that you are unsure of why to use one over the other.