I wouldn't clasify Mi Tierra's as romantic. It's touristy, loud, and bright, way fun at 3am after a night out or weekend morning.
There are many expensive, linen tablecloth, fro-fro, (not that there's anything wrong with that) places on the River (and other spots.)Here's my list:
Hotel Restaurants - Pesca on the River, Las Ramblas, Adam's Mark, The Landing, Anaqua Grill, Las Canarias Restaurant
Others on the River - Little Rhein Steak House, Fig Tree, Biga on the Banks, even the Palm or Paesanos
Away from downtown - Crumpets Restaurant & Bakery, Bistro Time, Silo, The Vineyards, Francesca's at Sunset