Go to your model, hit space bar, position the model so that you are looking normal to the face you'd like to be the "front" or "top" etc.... Once you've got your "new" front view, click on the button on the view menu that says "update standard views" then click "front". You'll get a warning essentially saying "are you sure?". Go back to your drawing, all the views should be updated.
On second read, I may not have addressed your issue. I see you are talking about making a template, my method is useful for already created models.
As far as templates are concerned, unless you have a "start part" with live geometry in it, you can just model the part in whatever orientation you need with the standard template. You could however, put in named planes so that you have a strong visual indicator to remind you of the orientation. If you'd like to do this, create a new blank part, add the planes and then go to "save as" and chose "Part Templates". Put this file into your templates folder.
Do you want to change axis only on part drawing or also in 3D?
To do it only on drawing you can rotate first view and then proceed to complete drawing.
If you want to do it on 3D as well, then if it's only for visual purpose then you can use method mentioned by Shawn,
else change sketch planes on already created parts to change their orientations and use correct planes and axis for new parts.
If there are multiple designers working on same project simultaneously, then I would suggest to create a part only with planes
and axis for each significant location and make it available to everyone in read only form, so that single person can control all
locations. I hope this part may serve as template you are looking for (probably to streamline design process)
Shawn Stugard was on the right track. Start a new Part with your existing template. Orient it the way you want (see How do I manipulate my model view; let me count the ways if you aren't familiar with how do do that), hit the space bar to get the Orientation dialog box, select the "Update Standard Views" icon, and choose the appropriate new view. Save as...Part Template (Why aren't the changes I made at Tools > Options > Document Properties saved when I start a new Part?) . Now any new Parts begun with this template should be oriented as you want.