What are the best places where crypto exchange could post a referral program? If it is bitcointalk for example, in which boards it is allowed to promote the referral programs? It also would be helpful to know if there are any other forums for this.
You mean announcing a program about refferals/(refferal program) that's hosted on your own exchange? You should be able to do that in your ANN thread just fine. I don't think there are any rules specifically against that.
But individually spreading/promoting refferal links is strictly forbidden, unless it is in your signature. See;
4. No referral code (ref link) spam.