Individual Romans traveled to China, at least. This old post from /u/Tiako talks about some Romans visiting China circa the reign of Antoninus Pius.

During the reign of Nero an equestrian was sent to the Baltic coast to acquire amber, according to Pliny's Natural History.

Pliny also writes about expeditions into Africa, such as Suetonius Paulinus, who might have reached as far south as Senegal.