Some useful websites relevant to Hove Park.
The Hove Park Management Plan is dated to run from 2009-2014. As far as I know, there is no more recent plan; the link takes you to a pdf.
The most recent rangers report of which I am aware is dated 2012-2013. This is the most recent (indeed, only) one on the council's web site; again, this is a pdf.
Like to dedicate a bench in the park? Or a tree? This site will tell you how much it costs, and provide much more information.
Brighton Museums has an article on the Goldstone.
James Gray Collection for the Hove West Blatchington Area has several old photos of the area. There are some relevant ones on other parts of the site.
My Brighton and Hove has several articles on Hove Park
Judy Middleton's Local History of Hove, Portslade, Brighton and surrounding area has 2 (interesting or relevant) articles. [Hove, Portslade and Brighton in the Past/The Goldstone] & [Hove, Portslade and Brighton in the Past/Trees of Hove] which includes (fascinating or detailed or extensive) information about the Great Gale & subsequent replanting.
Britain from Above has a 1937 photo of the greyhound stadium and Hove Park.
The Sussex History Forum has some prewar photographs of Goldstone Crescent and Woodland Drive, although you do need to register to view the photos. The Goldstone Crescent one shows the old line of trees before the Great Gale.
There is a 13 minute video entitled "The Storm of October 1987 in Hove Park Sussex" on YouTube.
Wanderlust676 on Flickr has a number of photographs of Hove Park with trees uprooted. The photograph that this link gives shows the telephobe box at the junction of Goldstone Cresent and The Droveway; now somewhat isolated, before the Great Gale it was hemmed in by trees and bushes.