How 'good' were the Ostrogoths as successors to Western Rome?

Did they rebuild any of Italy? Did they have an effective administration or literary tradition to help them rule their new territory?
Did they rebuild any of Italy?
Yes, infact if the sources are to be believed Theoderic rebuilt Italy quite substantially. To use the two biggest cities of his empire as an example:
  • In the capital of the Kingdom, Ravenna Theoderic started a massive building program. His ambition was to raise Ravenna to the status of Rome and Constantinople, a true Imperial City worthy of the name. He built a massive palace complex modelled on the Great Palace of Constantinople, lined with gold, marble and precious stones. The great entrance gate of his palace, the Chalke was faced with a mosaic of Theoderic, holding a spear and shield while flanked by the personifications of Rome and Ravenna. He also contributed to the city's ecclesiastical status by building dozens of new churches, for both the Arian and Orthodox communities. Finally, he restored Ravenna's aqueduct, originally built by Trajan in order to sustain a larger potential population.
  • In Rome Theoderic went on a massive building spree aswell. He restored the Temple of Vesta and the Theatre of Pompey. He restored the Palatine Palace which he would use as his residence while in Rome. He also followed his building program in Ravenna by erecting dozens of new churches.
Did they have an effective administration or literary tradition to help them rule their new territory?
Yes and no. Theoderic had an ideology of "Two people, one nation". Romans would be allowed to live by their laws, customs and courts while Goths would live by theirs. Thus since Theoderic left the Roman administration in Italy intact, the Roman parts of Italy went on as before. Northern Italy however had problems as it became the primary settling area for the Goths, which no doubt led to ethnic tensions and conflicts regarding the dual laws. Furthermore the Gothic customary laws were obviously nowhere near as uniform or robust as that of the Romans.

Theoderic tried carefully during his early reign to balance these two cultures, however as he grew older he became increasingly paranoid and would abandon this policy. He was preparing for a large scale persecution of Orthodox Christians, however this scheme never happened thanks to his long overdue death. Amalasuntha wanted to return to the tolerant policy of Theoderic's early reign, however her position as regent was weak and her imprisonment would serve as the casus beli for Justinian's invasion of Italy.