Vocabulary in The Love Song of J. Alfred Prufrock

The "eternal Footman" is a personification of death. A regular footman is a servant who generally admits and waits on guests—the suggestion being that if death is holding your coat, then you've entered a place where either you're not likely to come out or are on death's doorstep.

The phrase "sawdust restaurants" refers to establishments that have thrown sawdust over the floor to soak up spilled beverages and liquids. These restaurants are associated with "cheap hotels" and their sundry clientele. This walk indicates that the speaker is familiar with the red-light district, either because he lives nearby or because he frequents it for other reasons.