The diy guys have found that hacking a deep-freeze to run at fridge temps is ultra-efficient as all get out. The secret is that the top opens, keeping the cold inside the box. Remoting the heat source is near useless, as there is very little heat generated at all. Typical usage is 100 to 200 watt hours per day.
For a conventional, front-opening fridge with a freezer compartment, look at Bosch and Whirlpool.
Bosch has a euro-market line called the SmartCool. It uses like 60% less energy than regular fridges of comparable size. All the USA-market fridges have at least some of the SmartCool technology built into them. The SmartCool fridges are smaller than American models, because europeans in general have smaller appliances across the board.
Whirlpool won a 30 Million dollar prize for bringing a super efficient refrigerator line to market around a decade ago. They still get the best energy ratings. Check it out:
Best Refrigerator Comparison | Save Energy and Money at Enervee
But here's the punch line: none of these super efficient fridges are anywhere near cheap. As always, you get what you pay for.