Nice Blog! (I found you through a link on the Cool Cleveland website.)
My 90lb Lab/Malamute mix is in the camp with Dave's lab on size restrictions... ;) ... but as a west-side gardening enthusiast I have to say that I've seen many dogs at Gale's Westlake, shopping with their owners. Some of them are the 20lb fit-in-the-cart variety, but I've also seen a large St. Bernardish mix there that the staff seemed to know by name.
Take your dog to work day is this Friday, June 20th: http://www.takeyourdog.com/
Another pet friendly place is the Wine Bar in Rocky River. They have a doggie brunch on their patio every Sunday: http://www.winebarrr.com/fun.htm#DoggieBrunch
I have also seen dogs inside the Bier Market.
Note they DO NOT place restrictions on large dogs! My lab is offended at your attempt to restrict it to dogs under 20 pounds! :)
Don't forget about Great Lakes' Dog Day in July!
Anecdote: American Greetings Interactive does a bring your dog to work day in the summer.
I know it's an outdoor place, but you can also take your pooch to the Dairy King in South Euclid between Green and Belvoir on Mayfield Rd. Not only are dogs welcome there, they have a doggie treat for a buck. It's some vanilla soft serve on a dish with a dog biscuit on it. Cute. And my pooch loves it. Of course like all dogs, she loves eating in general ;-)
Dear goodness that is a cute puppy. Good to hear about Melt. I hope more places follow suit.
I used to dream of winning a lottery and opening a coffee shop/dog treat bakery where both species would be welcome. Now I just dream of someone else doing the work and me being a customer. West side please. LOL!