What are the moods for the chapters? What might be good songs that would go along with the moods?

Chapters 21 and 22 of of Book the Second of "A Tale of Two Cities" would be suited for Beethoven's Fifth Symphony as the tone of foreboding and the enactment of evil retribution is carried through both.  The repeated motif in Beethoven's piece can signify the title "Echoing Footsteps" of 21 as well as "The Sea Still Rises" of 22 as the music crescendoes.   

In Chapter 21  Lucie has a premonition of her "own early grave."  The footsteps that Lucie hears extend to the bloody town of Saint-Antoine where Madame LaFarge, "the revolutionary impulse incarnate"  The citizens storm the Bastille, slaughter its governor, rescue seven prisoners, and impale the heads of seven guards on pikes.  Monsieur DeFarge searches thoroughly the cell of Dr. Manette for an unknown reason.  The chapter ends,

For they are headlong, mad, and dangerous; and in the years to long after the breaking of the cask at Defarge's wine-shop door, they are not easily purified when once stained red.

In Chapter 22, "The Sea Still Rises," the men are "terrible, in the bloody-minded anger with which they looked from windows...and came pouring down into the streets; but, the women were a sight to chill the boldest as the aristocrat Foulon who told the poor to just "eat grass" is taken prisoner. As the crowd in their fury try to rend Foulon to pieces, he is finally hauled to a streetcorner where he is hanged on a street lamp with grass shoved into his mouth.  A drum that has rolled is now silent. Here a song witih drum rolls may serve to express the mood of Chapter 23 after the Fifth Symphony finishes.

The rhetorical chapter on the decadence of the French aristocracy, Chapter 7 of Book the Second is entitled "Monseigneur in Town."  In this chapter the tone is that of parody:

Monseigneur was about to take his chocolate.  Monseigneur could swallow a great many things with ease, and was by some few sullen minds supposed to be rather rapidly swallowing France; but, his morning's choclate could not so much as get into the throat of Monseigneur, without the aid of four strong men besides the Cook.  The mockery of the aristocrat who cannot swallow his morning chocolate without the aid of a number of servants can be parodied with the impressionistic music of Debussy.  "Afternoon of the Faun" may achieve this mockery with its mellifluous melodies.