Hi shootingstar,
don't fret too much. I don't own a cocktail dress nor an evening dress nor a formal dress of any kind. depending on locale, you may get a raised eye brow or they may refuse to serve you. Then again you are the one with the money so whooey to the snobby restaurant.
Boston, NYC, SF, Monterey, Carmel, if they say dinner jacket/blazer for men ... then you better plan on dressing up. Thankfully, these days, women can wear a dressy pant suit and get away with it. I typically wear my "power" outfit for my office for fine dining. My partner also wears a pant suit of sort. More artsy for her. We have never had any trouble being treated properly.
LA and San Diego lacks proper decorum so anything seems to go. I tend to dress business conservative or like a real slob. Not much inbetween.