I highly recommend Garmisch in Cable, WI. It's a lodge/resort just a short drive from Hayward. They have a beautiful location, tucked into the woods, and the restaurant overlooks Lake Namakagon. It has a perfect northern WI supper club atmosphere and they specialize in German fare and offer other supper club entrees (steaks, seafood, etc). Beats Famous Daves any day!
I completely missed your post and just posted myself on places in Hayward about an hour ago. Got home on Sunday night from 3 weeks visiting. I go a couple of times a year. For Famous Dave's, definitely try the weekend breakfast buffet - it is great! I didn't post about supper clubs in particular, but did put several recs there.
Agree that Robin's Nest is great for breakfast. I have to call my brother to find out the name of the other place we love for breakfast and my brother almost worships at the altar that is their burger. I am thinking it is Ray Jay's (will confirm and post).
As Rick mentioned, we also love Club 77 on 77 and Twin Lake Road (my brother lives down this road - it is the one of the roads off Round Lake, so I guess you will be staying somewhere near him). They serve a fondue relish tray. You don't find that here at home in Los Angeles!! ;-) Their Beef Stroganoff is fantastic and Rick, the owner, was telling me about the calamari filet that they make. Unfortunately, we did not have time to get there this time, but we did last time and that was when I had the stroganoff.
Angry Minnow is good, too. I always get their pretzel and their soups are pretty fantastic.
A few miles east of Famous Dave's on Hwy B is the Chippewa Inn, where we go for every year for our pre-Birkie protein binge (while everyone else is carbing up). This is your classic supper club with the lounge, the relish tray, the kitschy decor. The added bonus is the German specialties, including one of the best schnitzels I've had.
You might also try the Club 77 - the relish tray includes a cheese fondue, and the steaks were excellent as I remember (but it's been a few years). For lunch, I like the Angry Minnow brewpub in town (perhaps more for the beers than the food, though. And the food is decent). And for breakfast, you gotta get to the Robin's Nest on Hwy B just east of Round Lake. Great omelettes, and the best potato pancakes anywhere. Not cheap, but worth every penny.
10440 Florida Ave, Hayward, WI 54843