If you're sick of staring at screens, and don't want to get locked into an online game with some random guy online unless you absolutely have to (understandable), I thought I'd scribble out some of the stuff that's occurred to me over the years when I've been playing the game across two different editions of the game. It's important to remember that I am principally a Greyjoy player, and they've got quite a specific style of play.
The Golden Rule: Game of Thrones is a complicated game with a hell of a lot to think about. You can lose a lot of games getting lost in trying to be clever, so the most important thing to do at the start of every turn is to look at the board and ask yourself "can I win this turn?"
Deck Building - Game of Thrones has it's roots in the Magic: the Gathering school of needing to get some resource cards out to pay for stuff. It's less necessary as you have your plot deck to provide basic income, but you definitely want to be including more stuff, especially as the upper level characters are pretty expensive. Generally you want this sort of ratio for your deck: -
25% Economy Cards - this includes cards that you destroy to reduce the costs of these things. Stuff like Sea Tower is great, especially early on as it provides cost reductions for a deployment cost of zero. Generally I rate cost-reducers above +Gold cards because gold can be stolen, Cost-Reducers can't really be used by your opponent.
25% Low Cost Characters - I think for Second Edition, a "cheap" character is going to be between 1-3 Gold to play out. You never want to be without cheap characters to soak up military claim, and it's absolutely legitimate to include characters in your deck just to have them die in the place of the characters you want to keep. While there's nothing in 2.0 as crazy at this 1.0 Theon, it's fine for people to die. Generally I don't include multiple copies of my cheap uniques for this reason.
25% Higher Cost Characters - So this is the 4+ cost guys. These are the cards that you'll generally hinge your strategy on, and they need to be protected by your cheap dudes. Before you include multiple copies of these guys, consider whether you really need that many copies. Once they die, all duplicates in your hand become dead cards. It's best to include multiple copies of cards that you really need to draw.
25% Everything Else - This is quite a tight category for Attachments/Events/Locations, but having a flood of these things is a total nightmare.
... From this point, you just refine the deck through the usual process. Finding you're ending up with too much money with nothing to spend it on, take out some economy cards, etc. This is a large chunk of the fun of the game for me.
In terms of your Plot deck, there are a couple of things I always like to include: -
A card with some cash! Pentoshi is a great example of this. It helps your opponents, but if they're likely to be getting a smaller advantage than you! If you combine this with an Agenda like Red Door, it really helps you get your start customised to begin with. If you can get a couple of econ locations out as part of Setup, you can really come out of the gates fast by playing Pentoshi and buying a whole bunch of characters. Obviously, if you don't have any money, don't use Pentoshi!
A Reset - Valar or Wildfire Assault are excellent. If your opponent is pulling ahead of you, kill everyone. If you notice that your opponent has got a bunch of his super important characters out, then Valar. Kill them. Once they're in the dead pile, they're out of the game. Then you can start to come back.
Tutors - If your deck really hinges on some specific dudes or locations, tutors can really help with getting them out.
Consider a Stall - Calm over Westeros is a great first turn card if you want to build board position. Name Military as the conflict type and it means that your opponent will be reduced to claim zero and unable to kill your dudes. If the deploy a Claim 2+ card on the first turn, they're likely giving up a lot to do it, and you'll blunt it anyway.
A high initiative card - sometimes you really need to be able to go first.
Challenges Phase - This is of course where you're going to kick one anothers teeth out, so to speak. You'll generally want to approach this differently whether you're playing Melee or Joust. If you're playing a lot of Melee, please remember the golden Melee rule: Don't take the lead until you're ready to win on your turn. Melee games can rapidly turn into a "kick the leader" games - so just make sure you're doing that well.
Also for Melee, forget about honour. If you can win on your turn by absolutely savaging the player who's least able to protect themselves then do that. There's absolutely no reason to stand up to the big guys unless they're going to win if you don't. I've won a lot of games, and a few (local) melee tournaments by maintaining a slightly distant second place, wait for the winner to be kicked in, dropping my high initiative card the next turn and then wrecking him enough to scramble up over the Power threshold before he has had time to recover. If you're playing Melee with friends, it can be hard to do this, especially if somebody is having a bad game and they're not having fun...
... but it's Game of Thrones. At least you're bringing the game to a close, and they'll probably be doing it to you next game.
In terms of the actual challenges, you really need to think about the order you want to do them in. Military can make it harder for them to defend more challenges, Social can strip cards out of their hand they might try and ambush you with - generally I always do Power challenges last because they don't actually help the board state. If they've got a front line of big tough guys, then absolutely do not be afraid to poke at their front line with your Strength 1 starving peasant. You'll force them into a tough position where they either need to Kneel their Strength 5 powerhouse to block you (meaning they can't use it to hit you back), or you get an uncontested strike.
On the other hand, don't always feel like you need to defend yourself. The point is to win, not keep your guys safe. And so what if that Strength 1 Starving Peasant has to die to satisfy their claim? Let them walk through, and take it unchallenged. That's just more Power for your turn. Generally, I'm always happy to take loses as long as I know that when it comes back around I'm going to be hitting back harder. It's fine to let your opponent exhaust their top guys charging you unguarded lines. If they kneel enough you might just get three unopposed attacks back the other way on your turn.
This is why you need to have Claimbait chumps on the board at all times - to eat up this and leave your big guys to tear them apart on the return. The only thing to really remember is that lots of event cards activate if your opponent wins by 5 or more. So it can often be worthwhile trying to keep their victory to 4. But always remember, all that matters for the most part is that you got punched. How hard you got punched is irrelevant.
I've probably written more than you care to read already, so I'll shut up now, but if you've got any questions, please do come back to me on it! I'm really enjoying talking about this game because I love it so much. Just make sure you keep your eyes on that 15 Power victory condition. Everything else is just a resource to get you over the line - getting protective over your board state because you like the character rather than because they're helping you win is sometimes a mindset challenging to get past - Game of Thrones as a lot of great characters, and people include their favourites.
One of the people I used to play with always included John Snow as a triplicate because she loved the character so much and would always try and turn him into Voltron - I always did my best to kill him, because whenever I did she immediately went on Tilt and generally lost games because of it.