I prefer the N/W side of the peninsula, and based off of vacation homes and towns/destinations I'm gonna say a lot of folks share that opinion. Much prettier side of the peninsula. I mean I'd LIVE on either side happily if I could make the move permanently, but as a tourist I'm going on the N/W side.
Fitz's in Eagle River certainly meets what you're looking for in location. Good grub at their restaurant as well. They're wired a little differently than most sledders though, so you're sorta "behind enemy lines" doing business there.
In Eagle Harbor you have the Eagle River Inn. Good grub there too, but not right on the water. There's also Feltchy's Otter Belly Lodge which a sledder bought and re-opened up a year or two ago. He's right on the water next to the beach there. Also a dozen or so tiny cabins over by the lighthouse that are owned by various folks and can be found on vrbo or airbnb.
All kinds of options in Copper Harbor. None are right on the water really, but CH is where I'd go for a trip with just the wife.
Tons of options, including on the water stuff, via vrbo or airbnb in any of those three towns, or on the shoreline that connects them all. My wife and I spend a week at a place RIGHT on the water a few years ago called the Keweenaw Hodge Podge lodge. Quirky, neat place just around the corner from the Jampot and the monastary, just a mile or so down from the Great Sand Bay. All kinds of rock hounding can be done there literally not more than 25 feet from the back door.