The orthodox community is centered in two places, primarily: University City and Chesterfield. Chesterfield is a suburb outside of St. Louis. University City borders St. Louis City. It would not be walkable to the arch.
University City has many orthodox shuls. Bais Abraham Congregation, Young Israel, Agudah, UCity Shul and Chabad. There is a kosher Indian restaurant in U City. Otherwise, the kosher deli- Kohns, is in Olivette about 15 minutes from U City by car. There is also an orthodox shul- Nusach Hari – in Olivette. Many people would offer home hospitality for Shabbos.
Kohns also is a grocery store with all kosher food. Schnucks is the grocery chain and Schnucks in Ladue (which borders UCity) has an expansive kosher section with kosher meats and cheeses.