What am I doing wrong on Immortal level?

Thanks a lot everyone. The message is clear: food and happiness over production!
Time to play and play better!

Ok, so I won a sci vic (thanks everyone for your help!) on Immortal and I'm now trying for a domination vic. I thought following the city growth & happiness line while going straight for the Alhambra (after S.Zeus) would be a good strategy but other civs are beating me to it (the Alhambra). So, I guess that's not the way!

Should I get three strong cities, S.Zeus, forget the Alhambra and and go for M.Men before I capture my first city? I guess it depends on your neighbours, but I've tried with CB & pikemen and if your neighbours have elephants, for example, you're going to lose.

What do you think? Thanks in advance