The Soviets had several positive applications from their Peaceful Nuclear Explosion Program. These were mostly in the oil and gas industries and in the scientific sector. Tests of nuclear detonations for excavations were almost universally found to be useless - the craters dug were too radioactive for the uses intended.

Several explosions occurred to stimulate gas and oil production. For the most part, these detonations took place around the river Lira, north of the Caspian Sea. In the oil industry, this resulted in an increase of production of roughly 40-80%, depending on field. One project was carried out in the gas industry, detonating 6 devices, and resulting in an increase of production of 20 times normal. With one exception, the oil and gas detonations were contained, and no radiation was detected in the product. Detonations were also carried out to test the ability to make cavities in salt layers. These were intended to be used for storage of gas and toxic waste. While these explosions were initially successful, it was later discovered that these cavities tended to collapse, and to allow water in, both of which rendered them unviable in the long term. Finally, 5 detonations were used to seal runaway gas wells. All of these explosions worked as intended, sealing the well with no release of radioactive material

The Soviets detonated 39 nuclear devices as part of a deep seismic sounding program. This allowed them to measure the geology of the Earth down to 200-300 km below the Earth's surface, much deeper than can reasonably achieved by conventional techniques. They also detonated several devices to produce trans-uranic elements, but this was quickly superseded by the use of particle accelerators. In all cases, these detonations were contained, and no radioactive release occurred.

There's an excellent report on the Soviet PNE program published by Livermore National Laboratory, found online here, that I used for this.