Any IT specialists ever work for a hospital? How does it differ from other organizations?

Currently an IT Specialist at a VA hospital. LTC Broom highlighted one of the big components of life in IT at a hospital... information management and information security are huge deals, thanks to HIPAA. If you deal with a lot of electronic patient files, you will see a lot of security devices... cryptographic thumb drives and the sort. And trust me, they are not fun to deal with. You'll see a lot of equipment that you just don't see in any other environment, and you'll have to learn how it integrates with the network and systems. Your network, by the way, will likely be segmented a lot more than another organization of similar size. Your systems will likely be running on older OSes and programs, because those are sure to be secure for storage and transmission of PHI/PII (vulnerability assessment is a huge undertaking to roll out any new program version, even versions that are already outdated). And you are probably going to be operating with a subpar budget more than any other field's IT component.

Oh the health industry is very unique. I suppose it really depends on the details of the position you're seeking though. IM/IT within the health industry has a huge following. Healthcare Information & Management Systems Society (HIMSS) is the professional organization for people pursuing functional IM/IT career paths within the industry. Check out their website and see if they intrigue you. If you're a student, the annual membership is only $30. You may even be able to snoop around in their job bank. I'm not sure whether or not that requires a membership though. You can find it under the Professional Development tab (look for HIMSS JobMine) on their website.

http://www.himss.org/

Generally,PC support is PC support. The difference being the mission of the organization. In a hospital setting, things are usually more urgent than say, an insurance brokers office. When things break in a hospital, they need to be repaired ASAP. Unless of course SUNY is independently wealthy and is able to have a redundant system in ever corner!
I work in a hospital (the VA). I've been here for 3 years, and although I'm not a front-end PC Support Tech, I do deal with the clinical staff on a daily basis in regards to our Electronic Health Record (EHR) system. I've had to learn an entirely new language and learn how to write emails differently than when I worked in the banking world. Clinicians usually won't read past the third line of an email! :-)
There is never a dull moment in healthcare! Good luck!