I started having twice-monthly board game nights with my longstanding friends, where we gather together physically and play games. Originally, this was just to ensure that we stay active in each others lives, but I've found it's also useful for making new friends -- when I meet someone that I get along with, I invite them to join us.
I also make a strong effort to keep dating. The key to this for me is that I'm not looking for a serious relationship (but wouldn't resist one either), but just someone to go out and have fun with. I used to be very shy about asking women out, but that was because I was "looking for someone special". Now that I'm not, the stakes are lower and asking interesting people I meet out for coffee and such is much easier. Doing this keeps me circulating in social circles that I wouldn't be a part of otherwise. My goal is to go out on a date every week.
I'm kinda fortunate in that I am a passionate kayaker, and having your life be dependent on each other really helps create bonds quickly.