You cannot get HM08 Rock Climb until after you've defeated all of the Kanto Gym Leaders. Once you do so, Professor Oak will call you and tell you to come to his lab in Pallet Town, where he will give you the HM08 Rock Climb once you go there.
Once you get it, teach it to a Pokemon, and then immediately backtrack to these locations:
* Rock Tunnel (bring a Pokemon with Flash) : Lots of items including an Evolution stone and several hidden items.
* Cinnabar Island: Magmarizer
* Route 46 : Hidden Item PP Max.
* National Park: Shiny Stone and Cherubi in the trees on this ledge.
* Cherrygrove City: Hidden item Nuggest and Taillow in the trees on ledge.
* Mt. Mortar: Dubious Disc, Protector, several hidden items
* Route to the west of Ecruteak City: Burmy in the trees on ledge, several hidden items.
* Inside the cave in Cianwood City: Hidden item Big Pearl and Pokemon on the surface of the water.
* Route 47: Evolution item.
* Diglett's Cave: Rock Incense and several hidden items.
There may be a few more that I missed, but those are the big ones that you need to remember to go back to to get lots of unique items.
Hope this helps :)