I know a good number of Bases where there are Berry patches nearby.
I like to use the bushes in Route 120, the one with the capital "I" layout (see your game booklet, :P). But since there are no Berry patches there, a good Base could be the tree in Route 114, when you surf west and there's a little island with the tree. To the right, by Lanette's house, are three Berry patches. I like to use this Base too, since it's big and you don't need the Boards (I don't think Emerald offers Clear-out Sales...).
But I personally plant all my Berries in the Berry Master's Garden, so if you like, check the tree in Route 118. You do have to get past Wild Pokemon, though...
Try the tree in Route 111, where the boy gives you the TM43. Go left to the upper exit of Fiery Path and there are some Berry patches. There are also some to the north, just before you go to Route 113. You do have to cope with the small Base, though... :P