As Gralna said, Good King Moggle Mog the XIIth, Leviathan and Ramuh HM battles can all be ran as an 'undermanned party' - a couple of level 60s can trounce those fights.

As for the reason why access to Ishgard and it's surrounding areas is locked to story progression, that becomes apparent once you actually reach that part of the main scenario - the city is closed off to all but those of Ishgardian birth due to their war with the dragons, and it's in extreme and exceptional circumstances that the player becomes allowed to enter it (which I will not spoil).

Either way, the storyline explains why access to Ishgard requires said storyline to be completed.