See CMoS 8.168; see also CMoS 8.67
Romanise and lower-case the definite article in titles of periodicals.
the Sydney Morning Herald
Drop the definite article from proper nouns for venues, unless it is required for clarity.
If you don’t fancy the civilised nature of afternoon tea at the Windsor (Spring St), then…
Mercure (9205 9999; accorhotels.com.au; 13 Spring St; r from $115; p) The Mercure squats among lofty office towers…
The Pub (9011 9022; 95 High St) This English-style drinking house… [definite article retained to make it clear it’s the venue’s name, not a generic term]