Last year we sailed out of San Juan and it was from the Pan America Pier across from Old San Juan. The taxi was around $12 from an OSJ hotel. From what I have heard, if you are sailing r/t San Juan it will be from Pan America Pier and if San Juan is just a port of call on your cruise there is a chance you could dock in Old San Juan (depends on what ships are in port that day). Pan America Pier isn't walkable to OSJ at least I wouldn't.
I would recommend sailing out of San Juan to anyone.
Old San Juan has so much history, a lot ot the things I learned as a child I was able to see it.