Probably 80% of my work still targets pigment overlay on flexible substrates (hey, I just turned "print" into eleven syllables!), from flyers to billboards and just about everything between. The distinction between online and print was never very important: good design is good design, regardless of medium. Each has its different technical challenges.
For inspiration and ideas I just always stay alert for things that work well, whether I'm driving (billboards), walking around downtown, browsing a bookstore or magazine rack, visiting an art gallery or surfing the web. Those huge, wide billboards are great for web header and web banner ideas, by the way -- the design challenge is the same for both.
I seldom visit the big design/advertising industry sites and magazines. They tend to be behind the curve technologically while featuring what they think is "edgy" and "creative" instead of things that actually work (boost clients' revenues). You can assess from this my general level of respect for Cleo and Addy awards.
John McWade's famous Before & After magazine and blog are a constant source of practical and great-looking ideas. See this post as a fantastic example of "practical."
For technology I'm a regular at tv.adobe.com (since those are the tools I use) and numerous Adobe blogs and forums, Lynda.com (without which we would all be up the creek, these days), InDesignSecrets.com, PhotoshopUser.com (I've been a NAPP member for years, Mordy Golding's Real World Illustrator blog. I also from time to time may or may not be a tester for hypothetical future versions of unspecified products that may or may not be released by possibly well-known (or not) software companies at unspecified future dates. Or not.