I personally think "Table Top Games" is the most inclusive and strictly correct term that covers the scope of the site. It could easily include board games, card games, dice games*, and miniatures games. I believe that the best chance of getting out of beta may include a merger with rpg.stackexchange.com. I'm not sure how that community feels about it, but really, the latest edition of D&D goes back to its miniatures roots more strongly than ever. Roleplay is certainly in flavour with some Collectible Card games, even if it isn't typical for the players to actually "role-play".
There are certainly a wide variety of different games that are played on top of a table, generally seated, and many players of older and revered "thinking" games may chafe at the thought of casting a wider net, as might the casual card players, or hardcore rpg-ers… but I think the tent can be wide like Stack Overflow was.
If "Board and Card Games" or "Table Top Games" sounds clunky perhaps we can come up something evocative? There are several stack exchange sites that grew up to have their own name: superuser.com, serverfault.com, askdifferent.com, seasonedadvice.com
I was thinking that the majority of the games we talk about are basically turn-based, be they cards or board games. A phrase like "itsyourmove.com" or "itsyourplay.com" would sound evocative and be fairly instantly memorable. Alas, those domains were taken when I searched. Maybe a variation on that could be discovered?
Inspired by the granddaddy of these sites, stackoverflow.com, I thought something like tableoverflow.com might work. I'm imagining a logo with a table with two chairs, overflowing with game boxes, pieces, cards, poker chips, and so forth…
I took the liberty of squatting the domain, lest someone dastardly took it. If there is no interest in this idea, I'll just use it to host warnings of bad HTML table design or something… guffaw
* I've often wondered about this. Obviously questions about Yahtzee, Roll through the Ages, and even Poker Dice belong here. Are they, strictly speaking, board games? What about Mah Jong? Or Dominoes? Clearly they're of the same genre…