Try Crate and Barrel, I've always felt it is just Ikea at a higher price + quality. I suspect the price increase is greater than the increase in quality though.
There is definitely a gulf between Ikea (bad quality, good design, $) and DWR-tier places (good quality, good design, $$$$). Muji maybe, if they happen to make something in the niche you're looking for.
As the owner of several Muji items (trash cans, silverware holders, rolling storage unit, coasters, dish rack), I have to say while they look nice, they're rarely as well thought-out as Ikea. The trash cans don't seal, and the dish rack can't actually hold plates upright in position.
They don't do furniture, though.