I think that the Grand Basin at Forest park is a good answer. The Art Hill side overlooking the basin would be very romantic for a picnic, but not all that secluded. There will be people around.
Another idea in Forest Park if you want to be waited on would be the Forest Park Boathouse. It's over by the Muny and could be nice, although crowded during the summer season.
I guess it depends on your definition or romantic, but if you are looking for a park with a little less traffic than Forest Park, a few ideas would be:
Laumier Sculpture Park
Queeny Park - I know I've hiked up to a little dock on a lake here, but would probably never find it again if I tried.
Another nice view of the riverfront from a bar would be from the 8th floor at the Four Seasons hotel at Lumiere place. It's a nice rooftop patio with the hotel pool, and early in the evening it might not be that crowded. I know I was in on a Thursday and it was dead, but on a Sat night it was much more crowded. The drinks are kind of pricey though.