Stand in zones where the ball isn't and move accordingly but make sure you're close enough to see everything that's going on.
Around the middle or as close to the play as you can without getting in the way.
I'm going to buck the trend and actually answer the question. If it's 'proper' touch rugby (based on league), then you need to be on the defensive offside line. Depending on the rules you are using this is 5 metres or 10 metres back from the play-the-ball. You need to be here for a couple of reasons. 1) you need to show the defence where they should be 2) you need to ascertain for yourself where the defence should be 3) on the defensive line, the play is coming back toward you, this makes it much easier to see what's happening. Now get yourself accredited and ref some 15 man full contact rugby - it's great fun.
on the sidelines. You won't do much as a touch rugby ref, why don't you just join in?
Did you not learn this in refereeing training?????????? A bit concerned about your "whatever you call it" comment as well............did you do reffing training???????????????? You do know you have to have to have referees training no matter at what level and age!