Normalization and Breaking down tables for InnoDB
This is how I see it, it's better to have it separate, that's relational database 

If N User can have 1 address, the design should be:



if N user can have M address (user with more address, and an address for multiples user), should be:


For both design, the table USER, Column ID is the Primary key of that table, and User_id is just a FK.
In the second design, Table Address, column ID, it's another PK, that make a relation N:M with user, and create "user_has_table" with 2 foreign keys (user PK and address PK).