I would definitely recommend broadening the types of testing you are doing, as well as seeking out more complex functionality to test.
Have you ever done performance testing? Reliability testing? Security testing? Database testing? What about designing scripts that actually crawl the functionality of your website without you telling them what to do, and take screen shots as they go? What about fuzzing on those input fields? How can you create software that tests while you are out of the office and records interesting scenarios that you can then look at more closely when you get in the office? User246 mentioned API testing - this is, IMO, very good advice! API testing is actually quite easy, but often very intimidating - and you can provide a lot of value by testing from the API primarily, then only using UI automation for E2E tests and tests to make sure that the API is being called correctly (UI automation is expensive to maintain, so you generally want to limit how much you rely on it).
If you really want to focus on testing using Selenium, I would suggest sites where you do not create data but do interact with data in rich ways. Google Maps is great because there are complicated ways to interact, tons of data already there, and you as a user can do many things without entering text. Google Images could also be fun to work with. Instead of testing, you could also try writing small UI scripts with Selenium that, e.g., analyze metatext on a page. Maybe write a script to browse Coursera and find all courses with the word "software" in their title or description. Or maybe, automate a task you normally do manually. Can you create a small tool where you put in the date, time, and description for an event on the command line, and it browses to Google Calendars, logs in for you, and puts that event on your calendar? While you wouldn't do this in production code (you would use a Google Calendar API and not UI tools), it can be a fun way to build your skills if you really like UI testing.
Facebook is less good for testing than many Google products because so many interactions require you to enter information, which makes it expensive to test against (and could also result in you being black-listed if your behavior "looks" abusive). G+ or any highly social site will have the same problem. Think about sites you visit to get information, not sites you visit to give information. On the other hand, Facebook and other social media could be great to practice on to automate your everyday tasks - as long as you are okay with the risk of some very visible errors!
Make sure that, whatever you do, you think carefully about the effect your behavior will have on any live site that you are testing against! Not all sites can handle heavy traffic or random inputs without breaking. Testing against a major site like Google Maps shouldn't be an issue (unless you are spamming their APIs, in which case they will probably blacklist you), but a smaller organization may have bugs that could bring down their site if you test too hard. Be a good citizen!