As above, Skype and Factetime are generally not a problem in China unless your hotel Internet connection is particularly suspect.
General Internet access from hotels is really variable. It’s best to assume that you won’t have decent access to the ‘normal’ Internet, but you may sometimes get a (positive) surprise. The Great-Firewall-Of-China currently seems to be big into degrading service as well as blocking. So you would be blocked from accessing Google directly (Bing works OK), but may also be ‘punished’ by having your Internet connection slowed down to a snail’s pace for a short period. This really becomes a problem when you realise how many sites you normally visit contain at least some Google/Facebook/Twitter content which then result in you being penalised and pages taking a..g..e..s.. to load.
Sometimes VPNs are actively blocked – either you can’t establish them, or they’re torn down within seconds of opening up.
However, from time to time you stay in a hotel that isn’t, apparently, subject to any restrictions. I know of two big-brand hotels in random parts of China which seem to have Internet connections terminated in some way to avoid blocking – Google etc are all accessible and by default you get search results returned from Google.com.hk. I also know of one Chinese owned/run hotel which appears to have no filtering at all – although I have no idea why. Of course, the paranoid may assume that if there’s no filtering it’s because they want to see what you’re doing 😉