Replicate data of some tables of a local sql server to a database in Azure
My answer is assuming "we need some of these tables replicated on to a database on Azure" you are referring to Azure SQL Database.

First of all you need to make sure that you requirement can tolerate the generic restrictions with Azure SQL DB. 

Azure SQL Database resource limits

I did deploy these 2 methods with similar requirement you have.  Again you need to remember some of the on prem feature will not be supported.  


Sync data across multiple cloud and on-premises databases with SQL Data Sync (Preview)



  General limitations 
  
  
  A table cannot have an identity column that is not the primary key.
  A primary key cannot have the datetime data type. 
  The names of objects (databases, tables, and columns) cannot contain the printable characters period (.), left square bracket ([),
  or right square bracket (]).
  
  
  Azure Active Directory authentication is not supported.
  
  
  Unsupported data types FileStream
  SQL/CLR UDT
  XMLSchemaCollection (XML supported)
  Cursor, Timestamp, Hierarchyid
  



Transactional Replication.



  You can also use transactional replication to migrate a subset of your
  source database. The publication that you replicate to Azure SQL
  Database can be limited to a subset of the tables in the database
  being replicated. For each table being replicated, you can limit the
  data to a subset of the rows and/or a subset of the columns.