My Skyrim Mod picks, part II: fun game-like stuff.

There are certainly more good mods out there for Skyrim that improve the game itself; these are just some of the ones that I favor.  In no particular order:

• Falskaar. This is easily the most epic fan-generated add-on to date for Skyrim; there’s a coherent plot line, new spells, new Shouts, well-done voice acting, and the bugs are tolerable. The combat will stretch you, and the map (it’s a very LARGE island) is very, very pretty.  All in all, an excellent mod.
• Helgen Reborn. This mod, in my opinion, measures up to Falskaar in terms of fun gameplay.  The basic premise is simple: Helgen is in ruins; it needs to be rebuilt.  You’ll be doing this either in one fell swoop, or while you’re running around fixing/breaking everything else in Skyrim. The dungeons are well-designed (they actually managed to kill my PC a couple of times!); the voice-acting is professional-grade (as good as Falskaar’s, or perhaps that’s the other way around), and you end it with a new town to visit. The mod is also extremely good about integrating quest locations into the map without interfering with other mods, which can be a problem. If you have a choice between loading this and Falskaar, I might say load this one; it’s more seamless than the other one.
• Become a Bard. One mildly bizarre and slightly annoying thing about Skyrim: the world has bards. It has music. It has musical instruments.  It even has a Bard’s College, which you can join.  But you can’t be a bard. This mod changes that: it allows you to play in taverns, play for Jarls, do little quests for the Bard’s College, increase your Speech skill… that sort of thing. The mechanics are stable and the really nice thing about this mod is that the modder got the music from a bunch of people who write Elder Scrolls-themed music for the mod’s ‘songbooks.’ Which means that you can get your bard to belt out some pretty good songs .
• Granitehall, Laintar Dale, Oakwood, Amber Guard. These four location mods are from the same author, and are all based on locations in the first Elder Scrolls game (Arena). They are fully integrated into the map, and help fill it without overpowering it. Granitehall is an actual quest location; the rest are just places to get some smithing done, take a rest, and get swarmed by bandits. Nice addition to the game.
• Skyhaven Temple Glory and Nightingale Hall and Twilight Sepulcher – Improved. Both are revisions of faction headquarters to make them a little more nicer for your character to hang out at. They don’t go nuts on adding stuff, although Skyhaven Temple needs a bench outside for people to be able to sit down and enjoy the view.
• Dragon Knowledge. Turns Dragon souls into perk points (2:1 ratio). Since largely superseded by changes in the game (you now can spend excess Dragon Souls on resetting perks), but it was and is a nice thing to have.  This is, however, a bit of a cheat, so maybe not on your first playthrough.

Hope this helps!