The two things that come to mind for me are:
1. It's hard to find land lower than the ocean (https://en.wikipedia.org/wiki/List_of_places_on_land_with_el...)
2. Piping salty ocean water inland will make a lot of people unhappy. It would totally change the environment that was already there.
But interesting idea. Death Valley might be a valid place for it, since it's already a salty waste land.
The sum total of significant depressions:
* Salton Sea (~21700 km², sea surface ~70 m below sea-level)
* Death Valley (~13000 km², deepest ~80m below sea-level)
* Afar Depression (~200,000 km², average ~75m)
* Qattara Depression (~20,000 km², average ~60m)
* Lake Eyre (~9500 km², lake surface ~15m)
* Dead Sea/Jordan Rift Valley (total catchment area apparently ~40000km², below sea level probably more like 10000km², Dead Sea surface ~430m)
* Turpan Depression (~50,000 km², deepest ~150m) (note: quite far from the sea)
* Caspian Sea (371,000 km², surface ~20m)
There might be one or two basins the size of Lake Eyre I'm missing in the regions of Africa, but we're getting pretty shallow and small at that point.
By comparison, the total surface area of the oceans is around 360,000,000 km² (although I think that number includes the Caspian Sea, which is basically an ocean that's been cut off from the world's oceans).
Someone with access to GIS software could probably give you a good guess for the total storage of below-sea-level places on Earth. I couldn't find any calculations in my quick searching though, but the short answer is there really isn't much storage.
Overall, if it was a life and death situation not the worst solution in the world. We are probably good till 2050 and this could add another 12 years. We get 20% of our energy from nuclear and I hope both sides see the need for it and if we can get it to 60% and reach 300 nuclear reactors & cut down prices back to 2008 levels to $3B each and help China and India build theirs we should be in a great state.
The problem of course is that most of these lands are inhabited. You're just trading one parcel of land for another, one group of displaced people with another, one group of endangered species with another.
There's also the question of what you're going to do with all the salt water. You can't use it for agriculture or industry, you can't drink it, and desalination is extremely energy-intensive.
The Dead Sea, which at 1,200 feet below sea level is the lowest spot on the planet, had a proposed project taking water from the Mediterranean in the 80's [1], and has a current project taking water from the Red Sea [2].
The current project is slated to break ground in 2018. There is no way that several hundred million cubic meters of water per year will put so much as a measurable dent in global sea levels (there is some minor concern that there will be some environment impact on the Red Sea, but in- and out-flows between the Persian Gulf and the Red Sea dwarf the volume expected to be extracted for the project by several orders-of-magnitude.
So: Good idea, has potential for hydroelectric power in various locations around the globe, but no matter what won't affect sea levels at all, unfortunately.
[1] https://en.wikipedia.org/wiki/Red_Sea%E2%80%93Dead_Sea_Water...
[2] https://en.wikipedia.org/wiki/Mediterranean%E2%80%93Dead_Sea...