In response to Bortaxo's post I would agree on most points and can not stress how important Pricescope was (and is as we look at the bands). It really is the cut that matters. i can make the diamond look so much more brilliant and larger.
But, I'm not sure the costco diamonds are any worse (although I would not buy it mounted first). The same goes for online dealers.
This is what we did. We first went to standard B&M jewlers to figure out what she wanted. Then we did some pricing. Then I spent far too much time on pricescope so I undertsood the market and exactly what I was looking for. Then we shopped around. When it was an online dealer I made sure that they had a generous return policy (at least 10 days). Then I took the diamond to a independent appraiser who did not sell jewelery (none of that "well it's nice but I could sell you ..."). While I purchased the stone from an online jeweler, it was independently appraised by a GIA appraiser (who also happens to be a professor of gemology). Then i had the stone set by a local jeweler who i shopped at first. They could not even come close to touching the price for similar stones.
Note: my approach was made mcuh easier by the fact the I was looking for and bought a round brillliant solitaire. With some funkier design (round solitaire in a platinum setting is not funky by any means) it may make the process more difficult.