Hi Kevin,
If your cost/distance raster is static or defined temporally but independent from the model, you could use it to generate Transition Spatial Multipliers (http://docs.stsim.net/reference/prop_transition_spatial_mults.html) to set the probability of transitions for each cell.
If you would like to build in some feedback between modeled landscape dynamics and your cost/distance raster, you may be able to use the Transition Adjacency Multipliers feature found in ST-Sim (http://docs.stsim.net/reference/prop_transition_adjacency_mults.html). This is an advanced feature that allows you to change transition probabilities as a function of the state of cells within a neighborhood. So for example you could set the probability of an urban growth transition to be 0 when it has no urban neighbors within a 500m radius and increase this probability as a function of the number of urban neighbors within that radius.