I'll name a few of my activities, maybe some people can get ideas from them
Writing letters of encouragement; I have over a dozen pen pals, and I also write letters of encouragement to the elderly. I've been thinking of writing to prisoners or adopting a soldier or orphan as well. I use this as a way of witnessing of the truth. I don't bible-bash, but I have a Christian worldview and am not afraid to talk about Christ. On the way, I've found some amazing friends and great prayer partners.
Writing for the enjoyment and edification of others; I love writing stories, poems, and plays. I don't know if I'll ever get them published or not, but for right now I give them out to friends/family to read. I love to write a Christian story, or just some good clean fun. I would put any blogging, writing of pamphlets, and writing of newsletters under this category as well.
Writing for my own enjoyment and edification; I write a lot. I would put sermon notes, notes on the Bible/theological books, journaling, poems/stories that I do not show to others, and keeping a prayer journal all in this category.
Reading; I read a lot as well. Besides regularly reading the Bible through in a year, I read several theological books through in a year and a lot of non-theological books as well. Not all the authors I read are Christians. (gasp!). I do have a very strict view on what is appropriate and edifying, however. Most non-Christian magazines, (and a lot of books as well) don't make the cut.
Being in nature; This is my favorite! I love to garden, spend time with animals training them and loving them, hike, swim, play yard games with family and friends, watch the sunrises and sunsets, mow lawn, pick flowers, stargaze, the list is never ending! God is very good to give us such a beautiful world to live in, and He wouldn't have done it if we weren't supposed to enjoy it.
Movies; Ok, there's a lot of debate over this one in Christian circles. For me personally, I have not been convicted of any wrong in watching a few movies. I am very careful to limit my time spent in front of a movie (I personally limit to 2-3 a month), and of course, I severely limit the content. I think I've watched maybe 3 non-Christian movies that were made after 2000. Most of the movies I watch are older, or they're made by Christians; and even in those spheres you have to be careful.
Church activity; For me, at this point this includes cleaning the church, cooking the potluck meals, singing from the pews, welcoming guests (my sister and I are the only teenage members...we're pretty much on when it comes to trying to make the peer-dependent teenage visitors feel welcome!) and childcare. There are many things that need being done for a church to run properly, and the Bible makes it very clear that we need to all work together on this.
Music; Music and the arts, when used properly, are a great gift from God. I am not at all talented in any other of the arts, but I do have a small talent in music. I often play or sing at nursing homes, and go with a group that sings Christmas carols for shut-ins. I practice just for the sake of practicing, and pick up other instruments to try to learn just because I want to make music to the Lord in as many ways as possible. I also listen to a lot of Classical music. Not really into what gets billed as Christian music, and a lot of the modern stuff isn't good.
Serving the community; There are a lot of things to be done! I've recently been doing a lot of yard work and housework for the elderly. Look for needs, fulfill them.
Those are a few things, a bit to chew on anyway both for enjoyment and relaxation and service.