While not to encourage being antisocial, chess also has very good computer programs to play against--and even provide instruction. I assume there are good consumer accessible Go programs these days too although I haven't looked for a while. It's nice to have as a backup and, in general, I find computer card games are less capable or have annoying blind spots that you can suss out after a while. For example, I've found that computer Hearts programs are pretty vulnerable to shooting the moon against them.
Backgammon could be good--although I never really got into it. I suppose Checkers is another option but, of course, relatively simple.
Although I'm even worse at Go than I am at Chess, I agree with you. Chess probably has at least an easier learning curve to get to some minimal level of competence.