Where should I put nvarchar(max) dimensions in my data warehouse?
Microsoft recommends using a CCI for large data warehouse tables with a few caveats including:

Don't use a clustered columnstore index when:

The table requires varchar(max), nvarchar(max), or varbinary(max) data types. Or, design the columnstore index so that it doesn't include these columns.


Simply put, your options are to forgo columnstore entirely, create a nonclustered columnstore index on the table that doesn't include the VARCHAR(MAX) column, or to move the LOB columns to a separate table. You said that end users will sometimes access the tables without querying the VARCHAR(MAX) columns so I would try to use columnstore when possible so those queries can get the full benefit.
If I was designing this my first attempt would be to test your workload with nonclustered columnstore indexes that include every column except the VARCHAR(MAX) ones. That is a separate index so you will incur extra storage for the columns, but if you see the typical CCI compression ratio it will only be 10% extra. It's the simplest design and will put you in a good position to take advantage of SQL Server 2017's availability to include VARCHAR(MAX) columns in clustered columnstore indexes. Niko Neugebauer wrote a blog post about some testing on CCIs with LOB data in SQL Server vNext which you can find here.