Does a high-pressure system have a low-pressure or high-pressure center?
A high pressure systems has a high pressure center.
The rest of the solar system orbits a star (the Sun) which stays at the centre. To be precise, the whole solar system revolves around its center of mass. The Sun has about 99.85% of the entire mass of the solar system. So, its not surprising that the center of mass of the solar system is close to the surface of the Sun and that the Sun more or less stays at the center.