There is a sidewalk/path that connects Begg Blvd from the north to Kenwood Drive just above where it turns into Begg Blvd to the south. This is missing from OSM. It's reasonably clear in Google Satellite View: https://www.google.com/maps/@38.704416,-90.2762629,195m/data=!3m1!1e3!10m1!1e2

There is a missing (from OSM) public sidewalk/path that connects the north end of Stratford Avenue over two blocks to Kenwood Drive in a straight line. This is visible in the Bing satellite view, apart from the last bit that connects to Kenwood Drive: https://www.bing.com/maps?osid=35e7fdb4-a911-4401-a804-6777e787144f&cp=38.703011~-90.27629&lvl=19&style=h&v=2&sV=2&form=S00027 Here is the Google StreetView where it emerges onto Kenwood Drive at the north end: https://goo.gl/maps/34Xm7TZue1r7fenUA

This cul-de-sac is a private driveway for houses #16 and #17, not an extension of the road N Seminary Terrace.

Westerman Hall

There is a "hidden" paved path (sidewalk) from this point, through the woods, extending southwest to loop on Berkshire Drive (the entrance to the garage). It's faintly visible in Google Maps satellite view, but not marked in Google Maps either.

There is a "hidden" paved path (sidewalk) through the woods that starts at this loop on Berkshire Drive and extends northeast to St. Louis Galleria Street (the entrance to the garage). It's faintly visible in Google Maps satellite view, but not marked in Google Maps either.