Do you have to be a member of a church to donate to them? If they are helping parishioners, I would think they would take it from anyone.
Call your local police department (or that of the nearest good-sized town, and ask to speak to the domestic violence officer. Or call the National Domestic Violence hotline. Ask either/both if there's a local shelter who can use it - they won't give you the address of the shelter (safety reasons) but may tell you of a drop-off location. You can also call the phone store or the manufacturer to see if there's a program you haven't heard about. Believe it or not, there are programs that don't update websites, so sometimes a good old-fashioned phone call can get you more info than on-line searches.
Have you tried Freecycle? People pick up for free if they need the item you have - these are usually individuals and not organizations, so you wouldn't get a tax deduction but you would save the environment (a good thing!).
I just went to a program on Puerto Rico, and learned that there are 500 families in my area who have evacuated after 6 months with no power. They came with a few clothes and nothing else. So I've organized big donation collections of "apartment kits" for people finally getting out of FEMA housing and into apartments. I got a list of what they need and how to pack it, for families of 4-6 people. They need almost everything: silverware, dishes, pots/pans, coffee makers, pot holders, sheets/blankets/towels, you name it. I would think cell phones and laptops would be amazing for people who've lost everything to wind or flood or who couldn't bring "luxuries" with them. One of the people I'm working with is an area administrator for Catholic Charities - why not call one near you to see what they need?
I don't know of many charities that have money to send you prepaid shipping sleeves, but if you find one place that will take laptops and phones, the Postal Service has fixed rate boxes in different sizes: "If it fi, it ships." So while you'd have to incur some expense, you can keep i to a minimum. For heavy items like electronics, it's much, much cheaper to use this. Check with them first about requirements in shipping electronics though.