Get a mountain bike. This is a good 'one person' sport, but you can also go riding with other people.
I just started and it's not only really good exercise, but it's fun, relaxing, and there's a lot to learn. Trails range from easy and even paved to being steep and jam-packed with roots and rocks to dodge and hop over. The thing I really like is that you're focused on the ride; there's no time to think about being lonely or shut-in or any other problems like that. And it definitely gets you out...it's just you, nature, and the bike.
I spent about $500 for a decent mid-range bike made by Trek, but I imagine if you just wanted to try it you could get a less expensive one for $40-$70 off Craigslist or from Walmart and see if you actually like it first; just beware it might not last long on the more rugged trails. Alternatively, and I would recommend this more, most proper bike shops will rent you a pretty nice bike for about $40 a day. The benefit of a local bike shop is definitely worth the $$$ if you get in to the sport...they'll make sure you get a proper fit, they actually know about this stuff compared to Wal-Mart where the sales reps are clueless, and they can answer your questions and point you to a good starter trail.
If you've never been fishing, it's fun too. It's more of something to do to relax, though. My gripe with fishing is that if I'm brooding about something, or feeling depressed, sitting there casting my line and waiting for a fish just makes me think about it more. It's not quite as bad if I'm with somebody; so in that sense, it's not quite as much of an individual activity.
