Chrome just plain has this functionality nailed (I hate to sound like a chrome fanboy, but this is truth).
There is only one box, it's a combo location/search box. Type in a url: you navigate to that url. Type in a search string: you navigate to the search (using google or whatever search provider you designate) for that string.
I'm not sure if this is pre-release chrome 4.0 specific or not, but when you visit different sites (wikipedia, amazon, youtube, stackoverflow, etc.) the first time you perform a search on those sites they are automagically registered in your browser as available search engines. Then, to search those sites specifically direct from the address bar you simply start typing part of the site name/url, hit tab to autocomplete the search provider (much in the way the awesome bar works in firefox), type your search terms and hit the enter key. Thus, 'wiki+tab+napsack problem+enter' takes you to the wikipedia article on the napsack problem, and 'yout+tab+keyboard cat+enter' searches youtube for "keyboard cat" videos, and 'ama+tab+coders at work+enter' searches amazon for "coders at work". It's a very elegant, very practical design that I hope catches on.