Solid Hardwood, Engineered and Laminate Flooring - Which first, island/bar or floor?

This may be a silly question, but...

We currently have a vinyl floor, and are going to replace it with either a floating laminate floor, or tiles. The floor has some levelling issues, but mostly one 'trough' that runs diagonally, and produces a (roughly) 3/16" gap in the center. I realize I'll probably have to use levelling compound here.

We are also planning on installing an bar (I guess you'd call it that, an island with one short end attached to one wall). My question is, should we install the bar first, or the flooring? Or, is the answer different depending on what type of flooring we use?

My gut tells me to put the bar in first (and take the new floor height into consideration), but opinions would be appreciated.

If you put in the island 1st you will save $$ on the flooring and the height difference should not really be an issue unless you build the sub floor up around it . you should be alright installing the isl.