I would definitely recommend the new Tomb Raider (2013).
I always liked the series (although not a 'fan' of it either) and the reboot delivers. Also, Lara's animations are sublime and fluid, they transit so well and naturally between actions. I can't stress enough that the game's animations for characters are awesome (mostly Lara's as mentioned, but also enemies'). I don't know how much of them were motion-captured but it's just plain great to look at. The game's story is 'alright', there's some mysticism/esoterism thrown in and it adds to the overall mystery. I really like the pace of the game, although perhaps too linear for my tastes. But the game's events unfold rapidly enough to keep things interesting if you "keep going" and mostly play for the story progression, rather than the exploration there is to do (not that much to be honest, but there is some).
I'd also recommend Borderlands 2. I'd even say just skip the original. The sequel is better on every single aspects over the original's and more, in my opinion. Be it the story, characters and game-play. Especially the story, I mean BL2's story on its own it's exactly mind-blowing material (in fact I thought it was 'passable'), but in comparison to the first it's just a good light year ahead. If you haven't played the first but would still want to know what 'it was all about' I'd just say check its wikipedia/wikia pages to learn what happened (in the story) and from there just move on to the sequel. There's also a lot of DLCs (perhaps too many), some of which are worth it (most aren't in my book, but some are). It's definitely a very enjoyable game and can be quite addicting.
You said you like the Total War series, so if you haven't played it I'd recommend Shogun II, it's probably my second favorite in the series so far. I haven't played Rome 2 since I simply refuse to buy it (voting with my wallet, refusing to blatantly pay any amount of my earned money for an obviously rushed and bugs-filled game).
If you're into fighting games I'd highly recommend Injustice: Gods Among Us (especially if you like the DC universe, you know, Superman, Batman, Wonder Woman, Green Lantern, that sort of thing). You might have heard of it most likely, if not then it was made by NetherRealm Studios, the Mortal Kombat kreators (oh yeah, totally spelled that with a 'k', couldn't resist the temptation). And speaking of it, I'd also recommend their Mortal Kombat (2011) reboot, which is also very good (but I do prefer Injustice). I especially like how fighting games can be more than 'just that' with those two. There's a story mode, cinematics, and the inevitable on-purpose cheesy dialog and voice acting (in both), but really it's done in a way that's reminiscent of reading a comics (it felt as such to me anyway).
They are still fighting games, however, so of course even though there's a story mode in both you shouldn't expect too much out of that, they are good entertainment though. I just do appreciate that they took the time to put some more meat around the fighting genre bone. I do believe that not all fighting games out there are meant to also have a story mode, some are just plain good being just fighting games, period (although I admit I would like a similar story mode for a Street Fighter game). The 'campaigns' aren't mandatory by the way, they are optional and you can simply play both purely as fighting games, but of course if you play the campaigns you'll gain points to unlock extras (costumes, concept art, tracks from the OSTs, characters in some cases, etc). Oh and, obviously, if you play any of them... heck, if you play any fighting game on the PC make sure that you buy yourself a good pad for that purpose. I'm using the MadCatz Fightpad myself and I love it (not good for everything but good for fighting games, not the best though, but still I'm ok with it).
I'd also recommend Sonic & All-Stars Racing Transformed. I'm not really into other racing games like the Need for Speed, Grand Turismo, GRID or DIRT series. I usually enjoy racing games when they're based on fantasy or futuristic settings mostly (like Wipeout or Extreme-G for example), or if not at least if it differs from the more common ones. Give me a game where I can drive into powerups or accelerators laying on the road, give me crazy long-lasting tracks with things happening in the background as you drive, give me missiles, lasers or anything to shoot at my opponents and I'm happy panda. I've enjoyed racing games from series such as Mario Kart, Hydro Thunder (arcade), San Francisco Rush, Wipeout, Extreme-G, Road Rash (mostly due to the 'fighting your nearest opponent as you race' aspect) and Burnout. I can easily say that Sonic & All-Stars Racing Transformed is my favorite racing game since many years (also recommending to buy a proper controller to play it, at least with a joystick, because a D-Pad only for a racing game wouldn't be ideal).
I've purchased Far Cry 3 barely two days ago and only started it. I've played it for a total of maybe two hours so far. I know that most reviews out there basically praise it, despite the shortcomings (I also don't like to get a million tutorial pop-ups and not being able to save my progress "during a mission" even though I'm a dozen kilometers away from said mission destination in a 'sandbox' game). I did play FC3 on the 360 at my cousin's place before so I knew what to expect. So far I myself do enjoy it. To be honest when I first played it I actually expected significantly worse right from the start, but I was very pleasantly surprised. I do recommend it.
If you've never played them before I'd highly recommend both Saints Row: The Third and Saints Row IV. I like them both equally for different reasons and I honestly can't find anything to complain about... well maybe other than the fact that the game's map (Steelport city) is rather small for a 'modern' open world game. I haven't completed SRIV, but I did complete SR3 and it was an absolute blast. I also love the animations, the music, the voice acting, the dialog, it's all there and great, in my opinion (for both games). There's technically more things to do in SRIV, but I should point at the fact that there's a very active modding community for both games. I've used a couple of mods for SR3 and it does add to the content. Not all mods are good of course but some are worth it, notably the 'NPC Behavior and Spawn' mod which randomizes things to a new degree, making the game a bit more chaotic at times and less predictable (which for me is fun although that might not be everyone's cup of tea).
That's about it for my recommendations for now.