Ted Drews Frozen Custard... a delightful treat not to be missed. 6726 Chippewa St.
I was there once in the summer, waiting in a typically long line, when a wedding party pulled up and the bride and groom got out and waited their turn in line!

When you say "St. Louis" are you referring to downtown (The City), the nice(r) areas around it (The County), or the suburbs beyond?

Sometimes those are all described as "St. Louis", but each has their own offerings.