This is sometimes called a Zion psalm.
This psalm focuses on the city- 48:1, 2, 8, 8- Mt. Zion- 48:2, 11- Zion- 48:12- temple- 48:9.

But the ultimate focus of the city is on God- His greatness- 48:1- His protection- 48:3- HIs lovingkindness, righteousness, and justice- 48:9-11- His presence- 48:13-14. The praise of the city is the praise of the God who dwells there.

The city of Jerusalem represents something bigger. Gal. 4:26 speaks of the Jerusalem which is above.  Hebrews 11:10; 13:14 talks of a quest for a city whose builder and maker is God.  Revelation 3:12; 21:2, 10, 14 pictures the "new Jerusalem." This small capital represents God dwelling with man.

All that was intended by the city and the temple is fulfilled in Jesus- John 1:14; 2:19-22; 4:19-26.