What was Pope Sylvester's attitude towards Jews?

We don't know.
Reliable information about him is sparse. The claims presented in the question have to be called "wholly unfounded".

Important to distinguish anti-judaism and antisemitism. One is directed against the believers of a faith, assaulting this 'fasle belief* and trying to 'better' them by conversion; the other does that too but goes one step further and assigns an essentialist (genetic) trait to people, also defining them as a 'race', with often just eliminatory goals in mind.

Anti-judaism was widespread in antiquity, medieval and early modern times. Despite some remaining doubts towards them people under pressure of being a Jew could escape that by being baptised. 'Blind Synagogue' having lost another sheep to 'seeing Ecclesia'. With the advent of 'scientific racism' a simple baptism would not suffice anymore.

Seeing that pope Silvester was late antiquity, early medieval, his attitudes should be described as anti-judaistic. If at all.

Pope Sylvester I (also Silvester, died 31 December 335), was the 33rd Pope of the Catholic Church from 314 to his death in 335.[…] He filled the See of Rome at an important era in the history of the Western Church, yet very little is known of him.

Since legends and known forgeries don't count much, describing him as anything seems like quite the stretch.

As the Jerusalem Post article is now used as base for a horrendously sourced Wikipedia article:

The decrees of Nicea are here. They were authorized by Constantine. Silvester was not present at this council. More official decrees seen as harsh towards Jews around that time had not much to do with Jerusalem.

James Everett Seaver: "The Persecution of the Jews in the Roman Empire (300-428)" sheds some light on doubtfulness of exitant sources.

Steven J Katz: "The Cambridge History of Judaism. Volume 4. The Late-Roman-Rabbinic Period", Cambridge University Press: Cambridge, New York, 2006. Here: Chapter 38: Paula Frederiksen & Oded Irshai: "Christian Anti-Judaism: Polemics and Policies" (p 977–1034).
Note the page numbers of this standard reference work! It mentions Silvester – wait for it – one time, exactly:

In particular, the wave of so-called "public disputations" placed in legendary settings imagined capitulations of Jews to the new Christian imperial order inaugurated by Constantine. One such legend presented a debate between Pope Sylvester and twelve rabbis (accompanied by scriptural allusions, discussions of Jesus’ descent, and miraculous revelations), culminating in the conversion of 3,000 Roman Jews; similar themes characterized another fiction set in Jerusalem, the "Invention of the True Cross." While each of these stories may have originated in the late fourth century, their earliest redactions date from the fifth and sixth, and they circulated mainly in the East.

Were Jews at any time prohibited from living in Jerusalem? If they were, then they were before Silvester could have had a say on deciding that. It's commonly viewed that after the Bar-Kokhba revolt Hadrian forbade it. But were they, really?

Linder believed that one should not suspect the Christian sources of a one-sided attitude towards the Jews, and claimed that the prohibitions of Hadrian were meant to “ensure the completely pagan character of Aelia Capitolina by its total detachment from Judaism and the prevention of the possibility of its rehabilitation as a Jewish Jerusalem.”
In his view, the prohibition was in force until the third century and the beginning of the fourth century. But I do not accept Linder’s argument against viewing these sources as one-sided in their attitude toward Judaism.
The interpretative nature of the testimonies that attribute the fate of the Jews first by divine decree and then by the decree of Hadrian, places their historical value in question.
The conclusions of Rokeah that the Jews themselves refrained from visiting the city and that this is in fact the basis for the descriptions in the Christian sources clearly reflect the deep affront this caused to the feelings of most of the Jewish population at the erection of a pagan military colony in their capital — at the site of their sacred temple. There were some, however, who did not reconcile themselves to the bitter reality and settled within the city area, for example, that group of sages who, at the end of the second century, composed the “Holy Community of Jerusalem.” The establishment of Aelia Capitolina as a pagan colonia should not be interpreted as a punitive measure, mainly because the plan for its erection preceded the Second Revolt and was one of its incentives. The background for its establishment was mainly a political one, and it should not be given a religious interpretation.
_{Menahem Mor: "The Second Jewish Revolt. The Bar Kokhba War, 132–136 CE", Brill: Leiden, Boston, 2016.}

Even if we assume that Silvester had sway over Constantine's decisions, what were Constantine's decisions?

In 313, Constantine renewed the edict of toleration issued by Galerius in 311, thereby establishing parity for Christianity as an officially recognized religion (religio licita). For the Jews, this meant that Christianity was put on an equal footing with Judaism and was granted the same privileges (in particular, exemption from the obligation to participate in public sacrifices). Thus began the process which led to the eventual triumph of Christianity in Palestine, a triumph achieved at no little expense to Judaism. Under Constantine, Christian communities spread throughout Palestine, Christian pilgrimages became common (the earliest known account dates from the year 333 and was written by a pilgrim from Bordeaux), and Christian churches were erected at important Christian sites (including the Church of the Nativity in Bethlehem and the Church of the Holy Sepulchre in Jerusalem).
_{Peter Schäfer: "The History of the Jews in the Greco-Roman World", Routledge: London, New York, 1995.}

Claims about anything regarding Silvester, including the assertion that he was antisemitic, or anti-judaistic, have a lot of explaining to do, to convince any historian why these claimants believe unbelievable legends to be true:

Silvester

Bishop of Rome (31 January 314-31 December 335; the anniversary of his death is still named after him), probably a confessor in the persecution under Diocletianus. He received written communication of the resolutions of the first synod of Constantine (Constantinus 1 I) in Arles (1 August 314; Synodos II.); in it a Roman bishop is addressed for the first time as papa. Under S. the churches of Saint John Lateran and of Saint Peter came into being. He sent to the Synod of Nicaea 5 (325) only two priests (Vito/Victor and Vincentius). S. gained historical significance in legends: in the first half of the 5th century the Actus Silvestri (with a later appendix) appeared in Rome, their author claiming for S. the conversion and baptism of Constantine. The Actus Silvestri are also the basis for the Constitutum Constantini ('Donation of Constantine') of before c. 760.
_{Letsch-Brunner, Silvia (Zürich), “Silvester”, in: Brill’s New Pauly, Antiquity volumes edited by: Hubert Cancik and , Helmuth Schneider, English Edition by: Christine F. Salazar, Classical Tradition volumes edited by: Manfred Landfester, English Edition by: Francis G. Gentry. Consulted online on 23 May 2019 http://dx.doi.org/10.1163/1574-9347_bnp_e1113350 First published online: 2006 First print edition: 9789004122598, 20110510}