I prioritize my giving to local, small non-profits. I usually have a relationship with them beyond the check I write (I have volunteered or been a board member).
If you are giving to big charities (because they match up with your values), they have tons of data on what they are doing with the money. They also sometimes have internal funds you can donate to that are earmarked to only be spent on a specific activity -- just ask.
Good advice...I tend to focus on "local" needs, as well...you can often gauge their effectiveness quite easily because you can see efforts and results first-hand...
I've volunteered and served on boards, too...a great opportunity to connect with your "community" and gain a deeper understanding of the issues affecting it...
If you are giving to big charities (because they match up with your values), they have tons of data on what they are doing with the money. They also sometimes have internal funds you can donate to that are earmarked to only be spent on a specific activity -- just ask.