WJ -- Let me just say that I am quite jealous of your baseball trip. My work does not allow me the time to drive so many miles for my vacation, but I have many ballparks on my agenda (some scheduled already) for my spring/summer travels. We have a few overlaps -- Wrigley (two weeks from tomorrow), Rosenblatt (College World Series) and SBC Park (formerly PacBell) in late July. I also have (major league)trips to Busch (last year -- gotta make it!), Shea, Yankee Stadium, Network Associates (we planned our trip to SF/OAK when both would be in town within a couple of days of one another); and minor league stops at Sec Taylor Stadium (Des Moines, IA -- even if Rod Beck won't be living in his trailer behind centerfield), Billy Hebert Field (Stockton, CA), Muicipal Stadium in San Jose, CA, and P&C Stadium (Syracuse SkyChiefs). I also have enough $$ in bump vouchers from my last flights that I plan on hitting a few more missing from my list (Denver? Pittsburgh? SoCal?). People wonder how I don't have a girlfriend?

But, I am getting closer to all 30 ML parks now (almost easier to count the ones I don't have)...and it makes planning my trips a little tougher.
To bring this around to the topic of food.....
We did CWS in Omaha last year and loved it so much, we're heading back. I odn't know how good Johnny's could have been "in the past", but it was pretty darned good last year, and we plan on making a return trip this June. We also found an excellent Italian place (I know that doesn't meet your criteria, but I was surprised just how good it was....being from Long Island and all!) within relative walking distance to Rosenblatt.
I don't know if it is the absolute best, but a trip to Chicago should have to include a trip to "Superdawg" (which I am sure has been referenced on this sight a hundred times). I also plan on hitting the Billy Goat Tavern for a cheeburger-cheeburger, "pepsi, no coke", and "chips, no fries".
I will gladly update you upon my return for eats in SF area. We will be staying in Berkeley for four days, and plan on exploring the area thoroughly.
Enjoy your trip,
Steve