I know this is not a complete answer (yet!), but since I would like to post some screenshots, it is much easier to insert them here than link to upload pages that might get rid of the images at some point.
I am hoping to edit this post as I can figure out the solution with David. Anyone else, please feel free to suggest a wokflow or an alternate solution. I would be happy to add the screenshots in my posting!
You might also want to read the many comments below the question to get a clearer idea of what needs to be solved.
First of all, load your neighborhoods shapefile in QGIS. To do that click the following menu:
This will let you navigate to your file. Make sure you filter for shapefiles, so it is easier to find.
You will now see the file under Layers (top left corner). It is important that you save it anew and give it the correct coordinate system. As you want it to work with your lat/lon values, you would be using WGS84.
Right-click your dataset and go to Save As, and make sure to choose WGS84:
That saves your file with the right coordinate system. Now, you will add the file to QGIS. You can get rid of the original one (right-click: Remove).
Now you would want to add your CSV:
If you downloaded the file from your Google table, like I did, then you do not have to do much here. Just browse to the file and leave everything as is. Click OK, and make sure to enter WGS84 again.
Now your points will be shown ontop of your neighborhoods. To see the tabular data you can right-click either of the files and open their attribute tables:
You will quickly notice that the names of the neighborhoods do not always coincide, which might make the analysis a little more complicated, as we might have to edit the table(s).
Again, I will do my best to edit this post as we go along. I will think of a workflow and try to post it this weekend! If anyone else has suggestions, please enter them as comments, or add a new answer, and briefly note that it is adding to what has been discussed here.