We consider a service robot in a household environment given a sequence of high-level tasks one at a time. Most existing task planners, lacking knowledge of what they may be asked to do next, solve each task in isolation and so may unwittingly introduce side effects that make subsequent tasks more costly. In order to reduce the overall cost of completing all tasks, we consider that the robot must anticipate the impact its actions could have on future tasks. Thus, we propose anticipatory planning: an approach in which estimates of the expected future cost, from a graph neural network, augment model-based task planning. Our approach guides the robot towards behaviors that encourage preparation and organization, reducing overall costs in long-lived planning scenarios. We evaluate our method on blockworld environments and show that our approach reduces the overall planning costs by 5% as compared to planning without anticipatory planning. Additionally, if given an opportunity to prepare the environment in advance (a special case of anticipatory planning), our planner improves overall cost by 11%.