Flying Fig is an excellent restaurant. Unfortunately, I never have much reason to consider a restaurant based on whether it's romantic or not. It has romantic lighting and it's in a neighborhood with history and charm. I've had trouble keeping their schedule straight and I've been burned a couple times in the past. OpenTable says they're open on Sundays but it doesn't hurt to check.
fire is on the very-near East side. It's in another charming and historic nabe. With a little snow on the ground (*crosses fingers*) and the seasonal decorations, Shaker Square is as romantic as any place I can think of in Cleveland. The restaurant is all window and the view, barring the occasional fire engine, is always nice but really something special this time of year. The atmosphere is modern and understated, but I'd still call it romantic.
I'm sure they're open on Sunday.