Gardening is fun. It's nice to watch something bloom, grow, and flourish because you've taken care of it. And sometimes you can eat what you grow, too. If you get hooked on gardening you'll start seeking out all sorts of weird and exotic plants. To get started you really only need seeds, bulbs, or store-bought plants, a shovel, and lots of water and patience.
Birdwatching is fun, too. You can do it anywhere that birds can be found. So you can look out a window at your back yard, walk through a local park, or go to a migration hot spot at a peak time. If you get hooked on this, you'll start keeping a life list and start fantasizing about all the exotic places you could travel to... just to see some new birds. To get started you really only need your eyes and ears. Information can be found online concerning what birds look like and sound like (at least in the US). Eventually you'll end up with binoculars, a field guide or two, and maybe even a CD of bird calls.
Or you can mix the two and try growing a garden to attract some new kinds of birds to your yard. The best part? You'll still have plenty of time for other hobbies, too.