Clubs, as mentioned above, is a great way to meet people of all ages that have the same interests as you. I recently moved to Tbilisi, Georgia and although I have my boyfriend, I too feel the need for a friend. I've never had many, but the ones I've had were and still are wonderful. With an 8 (soon 9) hour difference, it's hard to keep in touch however. So, I too find myself alone some days. Just as an example, I've joined a language club. I'm taking Georgian classes and also teaching English classes to advanced students. I've met a lot of great people this way, and although no real connections have been made so far, it's still early on in our relationship. Who knows, maybe one friendship will blossom.
Another thing you could try is to force yourself to do things alone. Sure, it might not be as much fun and it might be a little intimidating sometimes, but I've met some wonderful people while doing things alone at very random locations. I met one of my ex boyfriends at Wal mart, for example. We were both browsing the magazine section solo. I also met an individual that greatly influenced my life while on a day trip, again, solo. It might be intimidating at first, to go out and pretend to have fun by yourself, but if you practice it a few times, you'll see you'll actually start enjoying it and you might win some great connections from it too.