Apple Blossom,
I know what you mean. I think you mentioned before that you are in Michigan, so I hope this info helps. Years ago I bought a book called Michigan Vacation Guide that listed places to stay in Michigan all around the Great Lakes from inexpensive cottages to more expensive B&B's and chalets.
My husband and I found a place in Paradise to stay called Birchwood Lodge. This was in 2003 I believe and we stayed for 4 days in a small cabin for about $250 for both of us. It wasn't the Ritz but we were right on Lake Superior.
Here is the link to a page that has the newest edition:
Michigan Vacation Guide I have the 1999 edition that is available on Amazon, but they don't seem to have the newer edition. Maybe your local library even has it if you don't want to order it from the site above.
And thanks for reminding me of the this book. I think I will order the new one to review for the site. Keep dreaming. I'm sure you will find a place for you.
I did some quick internet searches, but didn't come up with much. I will keep trying though as I know there are plenty of people who have the same question you do.