Those areas are perfectly safe to walk between, or you can take the people mover from Greektown to GCP. I would walk as it's not very far at all. If you walk down Monroe to Broadway and then up to the GCP area there's not very much blight and usually a lot of people around, especially with a Tigers game going on.

As far as cabs, you may find some in Greektown, or you could ask a bellman to call you one from your hotel.