Such a ponderous question cannot fully be addressed by one posting.  But, here are some of the most salient literary devices:

ANTITHESIS/THESIS

The very title of A Tale of Two Cities suggests this conflict of contrasts. The opening paragraph of this great novel employs this literary device which summarizes the major themes,

It was the best of times, it was the worst of times, it was the age of wisdom, it was the age of foolishness, it was the epoch of belief, it was the epoch of incredulity, it was the season of Light, it was the season of Darkness.... 

Antithesis also involves characters who both contrast and reflect one another. For instance, Mr. Lorry and Ernest DeFarge both work or have worked for Dr. Manette.  They consider themselves as businessmen; however, Defarge is unredeemed at the end of the novel because of his wife's hatred for the Evremondes, while Mr. Lorry's connection to the Manette family and the Darnays saves him from a life without love in Tellson's Bank.

Also, while Dr. Manette's experiences mirror those of Madame Defarge regarding the injuries dealt to her family, Madame Defarge is figuratively imprisoned by the evil of retaliation and he is "brought back to life" from his imprisonment in the Bastille.

DOPPELGANGER

Most salient among the doubles in this novel are Sydney Carton and Charles Darnay, two characters whom some critics feel are but two sides of the same psyche.  In fact, several times in the narrative, Carton reflects upon how he sees what he could have been in Darnay.  Their physical resemblance is what saves Darnay from a treason charge in England and death by the guillotine in France.  Of course, they both are in love with Lucie Manette.

Other doubles are Mr. Lorry and Doctor Manette; while Mr. Lorry has been imprisoned in Tellson's Bank [see Chapter 1 of Book the Second], Dr. Manette has spent fourteen years in the Bastille.  Both older men are reborn/resurrected by the presence of Lucie Manette, the physician's daughter, who helps to restore his mind and gives him a purpose to live and who also provides Mr. Lorry a family that he has never had.

SYMBOLISM

The red wine spilled in St. Antoine becomes symbolic of the bloodshed to come as well as foreshadowing "the time to come."

The shoemaker is symbolic of the imprisoned and mentally tortured Dr. Manette.

The Monseigneur symbolizes the effete aristocracy of France.

The stone symbolizes the cruelty and cold-heartedness of the Marquis d'Evremonde.

Madame Defarge's knitting symbolizes the methodical and insistent coming of the bloody French Revolution.

The Vengeance  is a character symbolic of the blood-thirsty revolutionaries.

The wood-sawyer is symbolic of Fate for the aristocrats in the form of the guillotine.

METAPHOR

Dickens uses metaphoric chapter titles to engage his readers who purchased this work in installments:

The night shadows are the inner feelings of people, inscrutable to others.  Sydney Carton has "old shadows" stirred up after meeting Darnay, for instance.

The jackal and the fellow of no delicacy are ironic metaphors for the nature of Sydney Carton.

The honest tradesman is also an ironic metaphor for Jerry Cruncher.

Echoing footsteps are the marching revolutionaries

loadstone rock is a metaphor for the magnetic ore that drew ships off couse.  (Darnay is drawn to France)

Tellson's bank is a prison

Another interesting rhetorical device that Dickens uses is the switch to the present tense as in Chapter 21 (bk. 2) to create suspense. 

The best way to respond to this question is to perhaps merely quote the first paragraph of this story and let it speak for itself. What is notable about this novel and the stylistic devices that Dickens uses is parallelism, which we can see stylistically enacts the relationship between the two cities, London and Paris, that the title of this great work refers to. Note the many examples of parallelism in the opening paragraph:

It was the best of times, it was the worst of times, it was the age of wisdom, it was the age of foolishness, it was the epoch of belief, it was the epoch of incredulity, it was the season of Light, it was the season of Darkness, it was the spring of hope, it was the winter of despair, we had everything before us, we had nothing before us, we were all going direct to Heaven, we were all going direct the other way...

The series of parallelisms then that open the novel introduce the way in which the fates of London and Paris are going to be closely intertwined and also foreshadow the parallel nature of so much of the plot. Characters resurface, such as Barsad, at critical moments, events are repeated, such as Darnay facing two trials, and images such as the golden thread and the shadow dominate this excellent novel from start to finish as the fate of Paris and London is shown.