Freddy,
Of course I am happy to help. I am from Jacksonville and know the areas pretty well. I have attached a map with the apartments I would consider. On the far left is the town center area (lots of shops, restaurants but also lots of traffic). Right next to Mayo is my preferred location (Hodges Blvd) some of the apartments are older but its a quieter street with a grocery at one end and Target on the other and very close to Mayo's campus. If you have a lot of money to spend and want to live by the beach I'd recommend ARIUM in PVB (Ponte Vedra beach). It's a high class area and very calm and quiet. I also know a few people who have lived in Banyan Bay on San Pablo. It's not on the map but it's an excellent complex as well.
This is mainly personal preference but I do not like Jax beach as much and wouldn't want to venture further towards Southside mainly due to construction/traffic. I hope this helps a little bit!