Cesar/Stephan, personally I have not seen much difference or I should clearly say any difference between a Dallas Restaurant site hosted in Dallas vs a Dallas Restaurant site hosted in New York. I just don't see any evidence today, but from a country perspective, it definitely plays a role. So if you were targeting Toronto Restaurants, the site hosted in Toronto/Canada would be better then hosted in Dallas/NY/USA. It would then also mean looking at a .ca domain vs a .com
However, this could change tomorrow and it would not be a big surprise if local hosting influences local rankings. So if you have the choice to host it locally, where your target customer is, do it. Expect no gains because of it today, but there's nothing to loose, right ?
As for Auto Suggest, yes, location plays a role. Just search for weather. You'd see your city's weather information. If you fly to another city and then refresh that weather results page, the results will change to reflect that city.
I hope this helps.