Okay, I started the Monkey Love mission in Zanarkand and quit half way through. I ended up walking around for a while as my original reason for heading out towards Zanarkand in the first place was to train so I could get past Yojimbo.

So I walk back to Yojimbo's cave and beat him and of course, get sent straight to the airship. I got the Besaid key and wanted to get my search sphere so I went to Besaid. I finished everything there and I can't use my airship.

So my question is: Is there a way to get from Besaid to Zanarkand without the airship? Or am I stranded on Besaid?

I'm not sure offhand. You could go down to the docks and see if the ferry is running. That could get you off the island at least. Otherwise I suspect you've got no way out.

another way to train is to dig in Sanubia. you get a lot of good items that can help you in the fight and such

Finishing all of the story mission there sends you back to the airship. You must've missed something.