Comment The Secret World, Star Wars: The Old Republic, F2P (Score 0) 337
As a long-time gamer & someone who's been in this same position of having a significant other far away, I suggest my favorite gaming genre- MMOs. They're social by nature & allow for collaboration. In terms of exploration, story, etc. that depends on the game. I'd suggest more of a sandbox type game. I just picked up The Secret World over the weekend (cuz it's 50% off 'til the end of the month!) for only $15. It's a "Buy To Play" title which means while it's an MMO, there's no monthly subscription fee, just buy the client & it's free forever after. TSW is a modern-day MMO w/3 playable factions- Illuminati, Templars & Dragon- & as you can guess by their names the story/writing is amazing & involves deep ties to historical events. So if you're both into history, like conspiracy theories & politics it'd be a great game.
Another GREAT story-based game is Star Wars: The Old Republic, it's "Free to Play" (F2P) which means you can download it & play it completely for free. Like TSW, SWTOR has great voice-over work & the choices you make matter & affect your storyline. It's set in the Star Wars universe but even if he/she isn't into SW, the story is amazing & all the different classes have very personal story lines that are extremely engaging. Aside from TSW & SWTOR, I'd suggest looking up any other F2P games as this new business model is king right now & there's literally TONS of games you & your significant other can play right now & engage w/each other. G'luck!