Raise high the roof beam carpenters! If you can, absolutely do it. Soffits can be disguised behind pseudo-stacked cabinets. You'll never regret the effort.

Ditch the drop ceiling if you can! What is under it...finished ceiling, rafters, water damage...the answer to that will affect "replace with what."

I would rather look at open space above cabinets or even bulkheads/soffits than a low drop ceiling.

Thanks. That's my instinct. No finished ceiling it is a first floor apartment with one above -- rafters and
fluorescents (that need to be replaced by, I suppose, high hats unless you have other ideas). The kitchen will be very contemporary -but it's a snowbird apartment and although I am putting in an expensive induction range, I'm going budget on everything else. Advice?

I don't know how expensive a coffered ceiling would be. We have one, though we didn't put it in because of a drop ceiling. Here it is: {{gwi:2142942}}