I’m the GM of a group that just started a long campaign and in a few months, I'm moving with my wife to a city 3 hours away from my current one. I'm wondering what the best way to continue playing on a weekly basis without having to drive down and back up.

If you use Discord, there is a Bot that can handle all the dice rolling, destiny point tracking, etc. It's not the best for maps and miniatures, you may have to look at Roll20 if you rely on that.

Are you the GM or one of the players? When one of my players was in the hospital for an extended period, I brought in a computer and he skyped in but he did say it got near impossible to hear when everyone was talking which does seem to happen a lot in our games.

EpicTable. Simple to set up a game with friends. Costs you $60, but costs them nothing. Sharing of images to a "game table", importing maps, drag and drop tokens, and even plain old school style playmats with digital markers. No FFG dice yet (I think the creator is trying to get permission), but that could be handled by other means. If you want more then text communication, then add Skype.

There are some others like Roll20 and Maptools, but they aren't nearly as simple. I've tried a bit of everything, but I'm currently in love with EpicTable if it's not evident.

ETA: Free to try for 30 days.

I've had good games with Roll20; Its fairly straight forward and the free version is capable of alot! (No need for any payment options in my opinion).

Pros:
+ Free for you and your players
+ Brings its own Voice Over IP Option (Including if enabled Video/Webcam)
+ Fully customizable Maps (you can upload images for maps, tokens etc., draw your own maps....)
+ You can hide parts of the map and reveal it as the players progress (but you need to do it manually)
+ You can prepare a boat load of scenes / Maps and move your Players easily into them, where they can (if you enable them to) move their own tokens and draw on the map.
+ Can be used for Soundeffects and Background Music
+ Comes with lots of different Systems (I'm not 100%, but I think I saw a couple of FFG Star Wars Sheets including Narrative Dice).
+ Players have their own sheets (which you can look into as well) and you can give them Handouts and the like.
+If needed, you can create Dice Rolling / Skill check scripts to further automate / slim down the mechanics of the dice rolling, but most Sheets you get on Roll20 already take a lot of work from you.

Cons:
- Has a Learning Curve (But I found it to be be relatively easy to get going as a GM).
- Some people have had problems getting the Voice Over IP to work (Scriptblocker's or Browser Issues, so we used Discord voice from time to time).
- Options like dynamic Fog of War (if you like such a thing) and a whole archive of tokens and maps is Premium Locked (but if one's interested in that, its not that pricey).

I havent tried Options like EpicTable, but Roll20 beats stuff like Tabletop Simulator or Google Hangouts by miles in my Opinion.
I've GM'd 3 Campaigns in Roll20 and have played in so many oneshots I cant even count them, I really like it.