Center of Rome which contained buildings temples and shops?

being a city, Rome has buildings all over its urban area, not only in its centre.

You do not specify whether you are referring to the centre of modern Rome or ancient Rome. The centre of modern Rome is the area between the the Pincian Hill and the river Tiber.

The forum civilium was the civic centre and the heart of a Romans city and its public, political, judicial and administrative life. It had a comitium, the place where the popular assemblies met to vote, public speeches were made and public debates were held. It had a senate house. Roman cities had their own local senate, moDELLed on the senate of the city of Rome. It had the courts were trials were conducted and administrative offices. It had public buildings (basilicas), shops, entertainments and important temples.

In the city of Rome the Forum or Forum Magnum as the Romans called it (Roman Forum is a modern term) which was a forum civilium, also had the aerarium (the treasury) which has in the temple of Saturn, the tabularium (the state archives) which was built on the slope of the Capitoline Hill, the regia (the residence of the Pontifex Maximus, the chief priest of Roman state religion) and the saenaculum (which was a place where the senators gathered before the entering the senate house for formal summons). It also had several platforms for public speeches. The oldest one was called the rostra (plural of rostrum). The name came from the six rostra (warship rams) of captured warships which were and mounted to its side. It faced the north side of the comitium towards the senate house. Later it came to be called Rostra Vetera (Elder Rostra) when other platforms were built. These were called rostra with the addition of the name of their builders or the person it honoured. The was also the Graecostasis at the southwest end of the Comitium, to the west of the rostra., The name refers to the Greek ambassadors for whom the platform was built after the annexation of mainland Greece. It became a platform for representatives of foreign nations and dignitaries from the Roman provinces (conquered territories).