When I tried typing in "upstate new york", it was replaced with "New York, New York United States", clearly not the region I intended. For now I'm just listing "Syracuse, New York", but I'd really like to specify a broader region than that, without having to list every major city in the area.
Right now you are limited to whole states, whole cities, counties, or zip codes. Would be nice to have phone number area code, and "region" option, or even a "within 100 miles of zip code/city" option.
The reality, though, is that in the database your locations are stored as lat/lon pairs, and it's the employer search that's important.
Ideally you should be able to enter "lat, lon, distance" which would give a very good flexible granularity, and would enable employers to search just as easily as they do now. You'd have to do more work on your end to convert "Upstate NY" to "lat/lon/distance" but you'd be in control of it.
Here are the details of how they actually use/convert the region into a lat/lon pair and bounding box:
There's no way, currently, for you to enter your own lat/lon/bounding box trio, but since it uses yahoo's query you might be able to play around with yahoo and find the correct regional entry to generate a single, or set, of bounding boxes that you like. I suspect that you can select a combination of counties and zip codes to meet your needs.
But you may consider simply including your local area, and then all of new york state. When in doubt, be inclusive and you can selectively reject offers for interviews outside your area.
You may enter counties as well, so how about using Onondaga County?
Yahoo maps will give you somewhat of an idea of the area: