The building in the distance is the Duval County Courthouse

erected in 1902 to replace the one burned in the 1901 Fire.

(And not to be confused with the similarly domed Jacksonville City Hall, hidden from view by the Bisbee Building)

Two additions to archfan's comment,

1) on the right -- the Hotel Seminole and whatever else was on this block of Forsyth Street have been replaced by the massive Bank of America building, and
2) the interesting dome in the distance is gone. I wonder what it was?

The photographer from the Detroit Publishing Company caught an interesting slice of life. In a quiet niche on the post office steps a couple is having a conversation which I believe includes romance. A small child wanders away from them. The man in white suspenders is sweeping away horse apples so the automobile, which is parked ahead of the carriage, won't soil its whitewall tires as it pulls away from the curb. A bicyclist is peddling towards the photographer as a man in a white Eton jacket runs across the street ahead of him and towards the post office. A collision seems eminent.

That looks like a brand new Packard Model 30 Touring sitting high and proud out front.

The two tallest buildings are still there - with several newer buildings between. The one in the distance looks like it has been shuttered for many years. The good news is that it looks like they're planning on refurbishing it into apartments!