I would like to measure voltage with an IC similar to the 7106 but I don't want all of the 7 segment display circuitry that it comes with. I just want to interface it to a micro so I can perform other operations beyond just measuring voltage. Does anyone know of an IC that can do this?
I'm not totally sure what you mean by "dual" though, but I'll assume dual-slope. Maxim/Intersil also makes a classic dual-slope integrating ADCs sans display, the ICL7135. It has (parallel but multiplexed) BCD outputs. (If you add a DM7446A to convert BCD you basically get the same thing as the ICL7107.)
Interfacing details depend on the [unspecified] micro you are using. To minimize the number of pins used, you'll probably want something using serial interface like I2C or SPI. For example MAX9611 has I2C and built-in current-sense amplifiers; it has fixed integration timings though.
Some (dual-slope) integrating ADCs like the Microchip TC500 (dubbed front-ends) have a custom 3-wire interface that requires the participation of the host MCU in the integration process (off-ADC timer basically). There are also ASIC "back ends" for these, e.g. TC520A which convert their output to serial port; the latter chip basically has the necessary state machine for the TC500, in case you don't want to bother implementing it on the MCU. The TC530 family is basically both of these chips combined, i.e. has built-in serial output. Alas the 530 has been end-of-lifed (but the 500/520 have not been so, insofar).
If you want a dual-slope integrating ADC with built-in UART interface, the ICL7109/TC7109 is still around; you can talk to UARTs even from the arduino family, either through hardware UART if available on the MCU or even by bit-banging (there's a library already written). The 7109 also seems the most widely available (in terms of number of distributors) among the ICs I've mentioned.
If you want to squeeze the best performance out of a dual-slope integrating ADC when helped by a MCU/processor, A 20-Bit (1 ppm) Linear Slope-Integrating A/D Converter (AN-260) from IT is worth reading.