Get a reservation at The Crow's Nest, the restaurant at the top of the Captain Cook Hotel. Ask for a reservation at table 38, the one in the corner. Nice view, but it's a view of the city. Anchorage isn't as nice as the landscape across the Cook Inlet. Simon and Seafort's a block away has a view of that. Any fine dining restaurant in Anchorage will have good seafood. A really good restaurant I like for special occasions is Jens's. But it's in a strip mall. If you are there around July 14, he throws an annual party that might make up for it. These are all fine dining restaurants, about $40-$50 per person.
Koots is a nightclub and bar. Actually about 10 bars under one roof.
Humpy's is a packed and loud popular favorite. Great place. But romantic? Not even. Just a good place to hang out, drink and eat.