Certain objects will not allow the stroke alignment options. Type is one of these objects. While creating outlines of type objects may work in some instances. I, myself, prefer to keep type live whenever possible.
In order to move a stroke applied to a type objects, simply do things how they were done prior to the stroke alignment options being added - with an effect.
Apply a new stroke to the type object via the Appearance Panel. Note you can't merely use the stroke which already resides within the Appearance Panel
Characters level of the type object. You need to add a new stroke outside the
Characters level. Then choose
Effect > Path > Offset Path.
Remember that Illustrator centers all strokes. So if you have, for example, a 4pt stroke and you want it aligned to the outside, you need to move it +2pts (half the stroke width). If you want it aligned inside, you would use a negative value (-2pt) to move the stroke inward.
That being posted, if you simply want stroke outside of the type, just move them below the
Characters item in the Appearance Panel and double the stroke width (since half the stroke will be hidden by the type).