@Steve_O One millivolt resolution in a 60 volt span means you need at least a 16-bit analog-to-digital converter. Adding ancient RS-232 communications protocol increases the cost somewhat compared to a USB solution.
Try this web page for a 16-bit A/D with RS-232 communications protocol.
If you choose the product cited on the web page, you will need to attenuate and then offset your ±30 VDC signal to accommodate the 0 to 2.5 V input range of their A/D. In other words, a 1:24 attenuation followed by a precision +1.25 V offset will do the job. Thus a -30 V input becomes -1.25 V, which then becomes 0 V after offsetting by +1.25 V. The +30 V input becomes +1.25 V, which then becomes 2.5 V after offsetting by +1.25 V. The A/D output then varies from 0x0000 to 0xFFFF as the input varies from -30 V to +30 V.
You should build a small circuit board containing buffer operational amplifiers and an IC-based precision voltage source to perform the analog signal attenuation and offset signal conditioning described above. Be sure to mount the circuit board inside a shielded metal enclosure to avoid noise pick-up. If at all possible, use precision resistors to perform the attenuation and to scale the offset voltage. Avoid using trim potentiometers if possible because they will introduce temperature-induced drift as well as noise from their wiper contacts. If a trim pot is unavoidable, its value should be in the range of one to ten percent of the value of the resistance you are trimming. That is, a 100 ohm trimpot is appropriate for trimming a 10 kΩ resistor, but a 1 kΩ trimpot is pushing your luck.
If you are comfortable rolling your own hardware and software, there are many A/D solutions that can be integrated with a microcontroller that implements an RS-232 interface. This would possibly be a "fun" project, but an off-the-shelf solution is probably a better idea.