This is really a question for our archaelogist friends, but I could not find an "archaelogy overflow" and some mathematicians might find it interesting.
In a few weeks I am giving a talk in which I would like to mention Archimedes' epitaph, which is reported to show a sphere and a cylinder. (Archimedes proved that the surface area of the sphere is equal to the lateral surface area of the cylinder with the same height and radius.) I realize that it is not possible to discover where Archimedes' epitaph was, or what exactly the representation was. (That is, whether it was inscribed, a sculpture, etc.) However, I would like to know whether there a location of Archimedes' grave which is consistent with
the description given by the Roman politician Cicero and also the 1925 century excavation report of the Italian archaelogist Paolo Orsi. In particular, is the description most consistent with these descriptions, that his tomb would have been under present location of the shopping mall "I Papiri"? http://www.centrocommercialeipapiri.it/negozi.php
Here are the two sources: (I realize that taking the word of a Roman politician at face value is a bit dangerous:)
Cicero describes Archimedes as being buried in a tomb to the west of the city:
"But from Dionysius’s own city of Syracuse I will summon up from the dust—where his measuring rod once traced its lines—an obscure little man who lived many years later, Archimedes. When I was questor in Sicily [in 75 BC, 137 years after the death of Archimedes] I managed to track down his grave. The Syracusians knew nothing about it, and indeed denied that any such thing existed. But there it was, completely surrounded and hidden by bushes of brambles and thorns. I remembered having heard of some simple lines of verse which had been inscribed on his tomb, referring to a sphere and cylinder modelled in stone on top of the grave. And so I took a good look round all the numerous tombs that stand beside the Agrigentine Gate. Finally I noted a little column just visible above the scrub: it was surmounted by a sphere and a cylinder. I immediately said to the Syracusans, some of whose leading citizens were with me at the time, that I believed this was the very object I had been looking for. Men were sent in with sickles to clear the site, and when a path to the monument had been opened we walked right up to it. And the verses were still visible, though approximately the second half of each line had been worn away."
(from Cicero (106-43 BC), Tusculan Disputations, Book V, Sections 64-66, translation provided on http://www.math.nyu.edu/~crorres/Archimedes/Tomb/Cicero.html)
The Italian archaelogist Orsi describes the exacavation of a Hellenistic necropolis from the 7th-1st century BCE to the west of the city.
"La necropoli del Fusco si estende per circa 2km lungo la rotabile di Floridia,
a partire dall'ex-osteria Rejna, attraverso le proprieta Corvaia de Gargallo (trappeto di S. Nicola e Tor di Conte) sino alla contra. Canalicchio prop. Carpinteri. All'inizio orientale di questa zona io ebbi la venture di scoprire un groppo di sepolcri, ancora in gran parte intatti, della fne del Sec. VIII e del VII, e po via via, procedendo ad occidente, quelli del VI e del V e piu la ancora gruppi del I-VI sec. av. Cr.
Rough Google-assisted translation: "The necropolis of Fusco stretches for about 2km along the Floridia carriageway (edit: not railway) including former tavern-Rejna through the property Corvaia de Gargallo (olive mill of St. Nicholas, and Tor di Conte) to the district Canalicchio prop. Carpinteri. At the east of this area I discovered a cluster of tombs, still largely intact, from the end of the eighth century and the seventh, and little by little, moving to the west, those of VI and V and still more the groups from I to VI century BCE."
(in NOTIZIE DEGLI SCAVI DI ANTICHITÀ – n. 4-5-6 (1925)
available at http://periodici.librari.beniculturali.it/visualizzatore.aspx?anno=1925&id_immagine=9999505&id_periodico=9817&id_testata=31
The reason that I suggest that the location most consistent with descriptions is the shopping
mall is that (1) Necropolis del Fusco is apparently the largest Hellenistic necropolis in
Syracuse, and so the most likely location of Archimedes tomb (2) it was, as in Cicero's
description, to the west of the city (3) the shopping mall I Papiri is at the end of the street "Necropolis del Fusco" in Syracuse, which runs through the area described by Orsi as the location of the Fusco necropolis, and the tombs from the later centuries are reported to be those at the western end.
Best Answer
In 1802 Johann Gottfried Seume visited Syracuse (from Germany per pedes). In his diary he mentions the place where Cicero had found Archimedes' grave: A chapel near the Greek theatre and the water pipe.
Johann Gottfried Seume: Spaziergang nach Syrakus im Jahre 1802 - Kapitel 35
EDIT
1) According to Seume's report this ruin is not the grave of Archimedes.
2) This painting by Benjamin West, showing Cicero and the magistrates discovering the tomb of Archimedes, is very popular but not very reliable.