I'm all for this idea, but I agree that for seasoned players starting a new game, advisor pop-ups can be annoying.
The idea of an Advisor Tab alongside those for Research, Spells, etc would work well.
It could also appear as advice underneath the report lines within your city overview.
Regardless, a good balance between Easily Accessible Advisory Information and YDHVYDWT, better known as You Don't Have To View It If You Don't Want To(tm) would be nice.