Like you said, making friends does take time. In my experience the best way to be in an instant new network of people is to attend a sociable, young, friendly church in your town.
Im not sure what your spiritual beliefs are...but if you truly want to make nice, trustworthy, caring friends, I would recommend going to a charismatic church in your area. There are always activities going on, and people love to make you feel welcome and socialize with you, go for coffees etc.
Trust me, I couldn't believe it when I moved to a new town and attended a small church in a theatre. My life changed over night. My misconceptions flew out the window, it was the loveliest group of people I'd ever met. Its a great starting point for you. Hope that helps...all the best!
