I'd certainly include all such information (ie, zip code, area code, placename, etc) on any page you're locally targeting, to pick up long tail searches that include these terms. The [keyword zipcode] query gets revised in Google, though, so... for Google, at least... what I say about zipcode inclusion may or may not be moot.
Whether you want to sort information and build target pages for neighborhoods, suburbs, or sparsely populated pages, gets into a number of very complicated issues concerning priorities vs population distribution in the US.
In general, on a national site, you'll find that, if geo terms are included in a search, it's mostly just metro area names that are searched. On local brick and mortar type searches, or in more sparsely populated rural areas, the variety of placename searches is likely to increase, but the numbers are very small. Search stats for prioritization are extremely hard to come by. As you note, zip codes and neighborhoods don't necessarily comform to each other. Even doing target-radius database queries (for visitors once on a site) gets complex, because the geographic lat-lon center may not correspond to the population distribution center point.
To agree with comments above, I too almost never use zip codes in searches.
And if so, do you think using the keyword in the META description would be worth while (multiple zip code in the description)?
A keyword in a meta description won't affect ranking. It may affect clickthrough if it's included in a search and you've sufficiently optimized your page to attract it.
Organically optimizing a site for multiple large suburbs in a metro area can be difficult, as you often run out of reasons to build separate pages. I haven't tried it for neighborhoods. Difficulty would depend on the popularity of the neighborhood name.
I just ran some local [keyword zipcode] test searches for sites I know that have placename optimization and don't mention zipcode, with my default location in Google changed to a place far away. Google's query-cop rewrites the query to [keyword placename], and a search "tip" at the bottom of the page confirms...
Tip: These results include the word "cityname". Show results that include only "12345".
It's not likely that such query rewriting would be neighborhood specific for organic serps. It might be for Place Pages. You'd have to try it in your metro area.