Good luck hope it goes well!
I have heard of couples praying the rosary together on Skype. Also, I think you could probably work out a way to play games together like chess or scrabble or things like that.
You might also try cooking together, each in your own kitchen. Or have one person lead the other person through some recipe instructions.
I have been in a LDR since March and we have FaceTime'd numerous times Here are some ideas:
2. Read the day's mass readings the night before and discuss them the next day
3. Show photographs of your family and friends
4. If you have a portable camera, show your living quarters
5. Read exerpts from Catholic-based books (Matthew Kelly, Scott Hahn, etc.)
6. Each asks a question that requires a thoughtful answer, such as "Who is your favorite saint and why?"
Good luck with everything!!
There's a website on the subject; sorry, I can 't find the link ... try 'googling' "Long distance dating ideas"
LDR's CAN lead to something special... Mine did, and may not yet be over; God has planted a seed that I can feel growing in my heart ... just can't tell what it is, yet.
OK, I know this is going to sound really stupid in the light of today's Skype/Smartphone world, but it worked great for my 5th graders to get to know the country's geography/ and for my 8th graders to get an idea of political awareness/trends in families scattered around the USA. It's based on the book, Flat Stanley, and each of you sends the other a photo of yourself (or makes a two-dimensional whimsical full-body drawing!) to take around for a week, as you go about your daily grind. You take photos of your "flat self"-- eating your breakfast, on the commute, with co-workers/friends, at the gym, at a volunteer event, at your church, with your family/dog/cat/neighborhood pals....and share with each other.
It's AMAZING how much information is shared this way! Crazy things like your recycling protocol, how you like your eggs cooked, what your favorite "after work stop" is, the weirdo who annoys you down the street, the person whom you sit next to at Mass,...Lots of great areas to laugh and learn from!