Hotels Downtown with a View

I’m going to be in Reykjavik for one night with two other people and want to stay somewhere downtown or walkable to city that is walkable to good restaurants and shopping and has the ability to sleep 3 in a room. I’d like to keep it under $350 per night. Something with a great sea view field be amazing but a great city view would be awesome too. Any recommendations? We are going in early November if that is relevant.