Minimum:
Search campaign
Add the area you want to target separately as an excluded region within you location targeting options for the campaign.

Use the adwords editor and duplicate your search campaign. Change the location targeting to just show ads to the region you excluded in your original search campaign. Change the ad copy to be geographic specific.

You now have 2 search campaigns targeted to different locations.

Maximum:
Do the above steps for your placement and content campaigns.

In your national search campaign (or a new nationally targeted campaign) use geographic keywords and geo appropriate ad copy.

Results:
One set of campaigns that reach everyone in the country except one geography.
One set of campaigns that only reach one geography.

Of course, you could do this for several geographies as well. Are you doing fantastic in in San Fran and always want your ads shown there? Give San Fran its own campaign with a very high budget.

Are you not doing well in LA? Go through the above exercise, and give people in LA more engaging ad copy to see if you can convert that GEO.

This works for both national and local companies. This exercise can be just as effective for eCommerce companies as for a location based company.

Hope that helps,
brad

Thanks!

Rod