Is it safe to leave most of your units in your borders and leave 1 units in the rest of your cities?

Always have strong defensive units in all your coastal cities.
Crossbows upgraded to Machineguns.
Musketmen/Riflemen/Infantry.
Axemen/Grenadiers.
Spearmen/Pikemen.
Triremes/Frigates/Destroyers

You can leave inner cities lightly defended if they are connected by roads/railroads and can quickly reinforce them.

It works for me, don't know about higher levels than prince though.

Military presents in cities also helps make people happy if you have Hereditary Rule as a civic.

Well, in my last game the AI only attacked my border cities. I play on pangae so I guess I can do that.

Generally yes it is okay. Just don't be to surprised if you lose one of your core cities. And coastal cities should be reinforced as well. Generally the AI won't bypass your outer cities but it can on occasion.

I play on immortal and I typically have border cities (and most of my cities for that matter) guarded by warriors/archers/axemen etc until MAYBE the modern era when I decided to upgrade them because I can.

Of course, if an AI declares on you, you should have known he/she was going to do that BEFORE they declared (WHEOOHN) so you should have a counter force ready.

What DMOC said. Warriors serve for a long time typically.