Skyrim, Fallout: New Vegas, and Mass Effect Legendary are my favorites that I come back to repeatedly. Of course, they were all probably perfectly playable on your old PC.
Hitman World of Assassination was good and not playable on your old PC. I have not replayed it yet, but it is definitely repayable with the option to approach every level in different ways.
I've gotten bored with the Assassins Creed games, but the newer ones are very pretty and they're open world with lots of story and tons of things to do.
You mentioned Far Cry 3, there's also 4, 5, 6 New Dawn, and Primal. I haven't played 5, 6, or New Dawn, but 4 plays the same as 3 (just a different story) and I actually like Primal quite a bit.
The Just Cause series is really over the top mayhem, but I enjoyed them. Lots of open world destruction for a...just cause (or maybe just because).
The Saints Row games are ridiculous, childish fun. Very similar to GTA, but makes GTA look classy by comparison. I think Saints Row 4 and Gat Out of Hell are the best ones. The first 2 are quite dated at this point. There is a recent remaster of 3, I liked the original, but haven't played the remaster yet. There's a newer one that's just called "Saints Row", I've only played a little of it so far and its pretty bland.
I think in 1995 my dad had pay by the minute internet access and I wasn't allowed to use it (and didn't really know what it was anyway). Somewhere around 1996/7 he got a dedicated ISDN line with unlimited internet and I stayed up all night talking to strangers in chat rooms or playing video games. Good times!