Can I position a pattern repeat tile within a shape like you can with the repeat tile in photoshop?
... however, it's not quite as visually dynamic as it is in Photoshop.
With the pattern-filled object selected, you can use the Direct Selection Tool (White arrow) and hold down the Tilde (~) key while dragging. The Tilde key (top left below the ESC key, left of the #1 key, on US keyboards) tells Ai to transform the pattern rather than the object. This works with the Direct Selection Tool to move, the Scale Tool, the Rotate tool, etc. Basically transformation tools.
Since not all keyboard may have the Tilde key.....
Another option is to use the menu...
Object > Transform... and untick the
Transform Object option and tick the
Transform Pattern option. To move, you'd obviously use
Object > Transform > Move...
(CS6 animation, but it's the same in newer versions.)