For which server you are reffering to ? Because each server has different regions.Johto-Hoenn-Sinnoh-Unova-Kanto.Also the difficulty of the gyms depends on your level of your pokemon so i don't believe there is an exact order of which gym you whould battle first.
Servers 3 and 4 include gyms from the original pokemon series, Rock, Water, etc. etc. The order goes Rock, Water, Fire, Electric, Poison, Grass, Steel, and Psychic. Each time you progress a gym, the gym leader's pokemon is increased by 10 levels, the rock gym being level 20, the water gym being level 30, and etc etc.
On the newer servers, I believe that different difficulties would change the level of the leader's pokemon. The first gym would have pokemon 5 levels above your highest leveled pokemon, the next difficult level would be 10 levels above your highest level, then 20, then 40.
The server 1 gym order would follow
Flying, Bug, Normal, Poison, Fighting, Steel, Ice, and Dragon.
The server 5 gym order follows
Rock, Water, Electric, Grass, Poison, Psychic, Fire, and Ground.
And finally, the server 2 gyms follow
Rock, Fighting, Electric, Fire, Normal, Flying, Psychic, and Water.