I've read the additional comments after my first response and I'm chiming in with more agreement

If your absolute goal is to be close the airport you are not going to have much choice in the way of 'walking neighbourhood'...the closest towns are not particularly 'destination' towns (ex SSF, Millbrae, San Bruno).

You can summarize it this way
1. Stay at a chain hotel like Hyatt or Marriott on the hotel strip south of the airport. No 'neighbourhood' feeling at all but you can walk from hotel to hotel.

2. Stay at a buget hotel in SSF, Millbrae or San Bruno. Will be able to walk to restaurants but your choices will still be limited for both restaurants and hotels. Not exactly a neighbourhood.

3. Stay at a chain hotel and go to downtown Burlingame. It has nice restaurants, cafes, stores. If you have breakfast or brunch in the area, go the Copenhagen bakery. I love their 'pancakes' with lingonberry sauce.

4. Just stay in the city. The Palace Hotel is fantastic...a historic starwood property close to the Modern Art Museum, Union Square, lots of restaurants, walking distance to the Embarcadero...and close to BART which will take you right back the airport. I agree that you should avoid Fisherman's wharf at all costs.