Yes they are hard to find like that. We live in a 3/4 bedroom "vintage" log house and we are about 6 miles from the closest lake. We looked at others before we "re-built"/relocated this one and did not see to many.
Actually, the one we live in now, part of it was originally at a lakesite from back in the late 1700s. Most of the property was swamp land though.... which I would have liked.
My dad has a friend that lives in Kingsport, but he has a recently built log home with a back yard creek on the southeast side of Bristol TN. Its a very nice home - again, the old vintage square logs, but its built with all of the latest conveniences and is a fine home. I am not sure if he would sell/rent it, but I will see if he can get ahold of him and ask or if he knows of any.
Good luck on your search!