If I am understanding what you are trying to do correctly - You want to find the spatial relationship of different geographic areas. You can use geoprocessing tools such as UNION or MERGE to get the output of relationships between the areas. Do you have access to ArcMap or ArcPro also you can download QGIS and use for free. Yes Metropolitan Statistical Areas are counties and multiple counties. Yes places are a level under counties kind of. Census Tracts are a step below counties and Block Groups are a "step below" Tracts. Places aka cities and etc can cross counties, MSAs etc. So probably you want to CLIP the PLACES by MSA Then UNION and SUMMARIZE while DISSOLVING places by msa. ---> [7 essential Geoprocessing tools][1] <----


  [1]: http://gisgeography.com/geoprocessing-tools/