Cityfreak, what a double blow for you - your ex was also your best friend. What bad luck!
I think the dating agency/internet site solution is definitely one way to go. If this site is anything to go by, there are lots of nice, non-wierd people out there. Do you log on to friendsreunited? What about organising a class reunion or emailing some of your old school or college friends?
But running alongside this, I think it would be good to look for a new boyfriend in a more non-specific way. IME one surefire way of meeting men is via friends and acquaintances. The more friends you have the more social invitations come your way. Also, the men you meet via this route may be very well known to the group you are with - an invaluable safety net. And, if you meet a man and it doesn't work out, you've still got your new friends to fall back on. One big advantage over dating agencies. You're not putting all your eggs into one basket.
So, I think you should investigate group activities that appeal to mixed sex twenty - and thirty-somethings - like a sociable sport, a book club, a film appreciation society, a car enthusiasts club, a sponsored cycle ride. I read a great newspaper report recently about professional city people who do a few hours voluntary work each week eg for a hospital radio service. Each interviewee said one of the major benefits was the great social life attached to this work, and the friends they had made through it. Worth considering?
Also, hope you don't laugh at this - I know you work full time - I don't know what your home area is like, but have you considered getting a one or two night a week evening or weekend job, if babysitting allows? Some careful looking might reveal a nice local meeting place were there's a good chance of broadening your social life via fellow workers or clientel. ie a local theatre, cafe/wine bar, music venue etc.
Anyway, these are my suggestions. Hope they help!