Incidentally, are there dress rules for attending a synagogue? I know men have to wear some sort of headgear, but is it basically business suits? Or can you wear casual / smart clothing?
It varies with the synagogue and branch of Judaism. The occassion also plays a role.

My wife is Reform. When we go to services with her parents, I can usually get away with dockers and a button down shirt. I don't even have to wear a yarmulke most of the time. The High Holy Days have a stiffer dress code though and suits or sportcoats are the rule.

Parts of her family are much more Conservative, bordering on Orthodox. When we attended her young cousin's bar mitzvah, it was business suits complete with a yarmulke and tallis (the prayer shawl). Fortunately those were traditionally provided on site.

I told my wife I was going to wear my kilt the next time we were invited to a black-tie optional wedding on her side of the family. She was not amused.