At what place are inscribed the the words "Give up hope all ye who enter here"?

The short answer: Hell.

Dante's Inferno (part of "The Divine Comedy," by Dante Alighieri) is
the source of your quote. According to Dante, the Gate of Hell is
incribed thus:

"Through me you pass into the city of woe:  
 Through me you pass into eternal pain:  
 Through me among the people lost for aye.  
 Justice the founder of my fabric moved:  
 To rear me was the task of Power divine,          
 Supremest Wisdom, and primeval Love. 
 Before me things create were none, save things  
 Eternal, and eternal I endure.  
 All hope abandon, ye who enter here."  
 Such characters, in color dim, I mark?d         
 Over a portal?s lofty arch inscribed. 

Bartleby: Inferno [Hell] Canto III 
http://www.bartleby.com/20/103.html

Dante's original poem was written in medieval Tuscan (a dialect of
Italian). There are many ways to translate the famous line.

"Dante faints and does not awake until he is on the other side and
approaches the Gate of Hell, on which is inscribed the famous phrase,
'Lasciate ogne speranza, voi ch'intrate' or 'Abandon all hope, ye who
enter here'...

There are many English translations of this famous line. Some examples include:
 
Abandon every hope, all ye who enter (Mark Musa) 
Abandon all hope, you who enter here (Robert Pinsky) 
All hope abandon, ye who enter here (H.F. Cary) 
All hope abandon, ye who enter in! (Henry Wadsworth Longfellow) 
Leave all hope, ye that enter (Carlyle-Wicksteed) 
Abandon every hope, who enter here. (Allen Mandelbaum)." 

Wikipedia: The Divine Comedy
http://en.wikipedia.org/wiki/The_Divine_Comedy

The phrase has appeared in various forms in many media, ranging from
the text adventure game "Zork" to the novel "American Psycho."

My Google search strategy:

Google Web Search: dante hell hope "who enter here"
://www.google.com/search?hl=en&q=dante+hell+hope+%22who+enter+here%22

I hope this is helpful! Please let me know if you need anything
further. I'll be glad to offer additional assistance before you rate
my answer.

Best regards,
pinkfreud

pinkfreud is as impeccable as usual, but I could have sworn it
appeared over my local IRS office...

Yes, an easy joke but then I'm an easy guy (who's in for a serious audit).

>> I could have sworn it appeared over my local IRS office...

Perhaps you were been thinking of the INFERNAL Revenue Service. ;-)

Please forgive my embarrassing typo in the comment above. Instead of
"Perhaps you were been thinking," my remark should have read "Perhaps
you were thinking." Apparently I was NOT been thinking, or I wouldn't
have done did this.

Another potential answer which occurred to me, "The gate to
Auschwitz", is debunked at
http://www.dcwatch.com/themail/2000/00-08-02.htm
and elsewhere, no doubt. 

I had to search for "abandon hope" to find it. 


   ?Abandon Hope? at Auschwitz

   David Sobelsohn, dsobelso@capaccess.org

In the most recent issue of themail, Thomas C. Hall writes that
?'Abandon Hope, All Who Enter Here' read the sign atop the wrought
iron gate to Auschwitz.? Although Auschwitz was a pretty close
approximation to Hell, the ?abandon hope? line actually comes from
Dante's ?Inferno.? The sign over the entrance to Auschwitz actually
read (with truly evil irony) ?Arbeit Macht Frei? (?Work Makes You
Free?).

The original: Lasciate ogne speranza, voi ch'intrate, suggests that
the translation should be 'abandon all hope, ye who enter'. The
English version asked about is found over Traitor's gate in the Tower
of London

Dante's Hell is the answer, as well documented by Pink Freud.
Auschwitz and the Tower of London are sometimes mentioned, but
inaccurately so.

Regarding the comment above about the Traitor's Gate, I have found no
official confirmation that there is, or has ever been, such an
inscription there. What I have found are several apocryphal and joking
references such as this one:

http://pics.livejournal.com/2ndavemusic/pic/000267ry/g9

Tours of the Tower, given by a Beefeater, include the information
about the inscription being on the river-side of Traitor's gate, since
that was how the prisoners came into the Tower. I admit I never took a
boat to check it out, so it may be apocryphal. It certainly would have
had to be added after Dante's writing

If the text were over Traitor's Gate, I expect that this site would
have mentioned the fact.
http://www.toweroflondontour.com/gatewake.html

Although the gate was called Traitor's Gate in QE I's time, it was
probably used for other purposes, since it was the water-gate to the
Tower of London and the most convenient entrance for supplies.

If the words were/are there, it would have been placed there sometime
after the first transalation of the first 3 cantos (canti) by Jonathan
Richardson in 1719, but more likely after Henry Cary's translation in
1814, said to have made Dante's work popular.  Carving or painting
such an inscription could be in line with Victorian romanticism, but I
still think we could find reference if this were so.

Scroll down to footnote 16 after the red bar to find reference to Richardson.
http://demo.insitemedia.hu/theanacronist/html/1998/macsok.php