I totally understand that it's hard to do things alone. I'm a shy person myself. Well, my friends don't think so but when I'm alone in a new situation I would just assume blend in with the walls. But I have had so much fun trying new things. Surprised myself since I thought I would have a hard time smiling and laughing again.
I started going to a sports bar to watch football. Made some new friends and got some much needed male attention. (But I was there to watch football and I didn't date any of the guys I met.) I also went to a concert alone, ended up talking with the guys sitting next to me, and went out for a bite to eat with them after the show. Turns out the company they work for has an office in the area I'm looking to relocate to so it ended up being networking too.
Started taking dance classes. Always wanted to tap so figured now's the time. Also taking a strength and flexibility class filled with 16-22 year old dancers. Hah! But it is fun and good for me. I took yoga for a month but then got lazy when the first session was over. Need to get back into it because I found it good physically and mentally. Also started teaching myself piano but gave up because the room the piano in is unheated in the winter. No more excuses now that the weather is warming up. I meet up with a girlfriend once a week for happy hour or dinner. I have lunch with another girlfriend every week or two. I have plans to join a bookclub. And I have a policy of not turning down any invitation. I've been to a trailer trash theme party, a makeover day, country dancing, and concerts.
Sounds like you have some good ideas. Museums always have lectures and events. I hate cooking for myself too, but a cooking class is a good way to get started. I'm trying to find one of those myself. And meetup is a great idea! I haven't tried it yet because I planned on moving out of state, but may have to look into it now.
Ok, hopefully that helps motivate you!
If you love somebody, set them free. http://tinyurl.com/2empx2g