Places like Harvard will have great research / resources in a subset of the areas in an engg major, and less coverage in other areas. If they are interested in the areas you are interested in, you won’t find them lacking. They will be state of the art. Plus the usual Harvard reputation will help you find jobs etc. Since need blind is a significant consideration, you could also consider Princeton.
If you are going to consider Purdue (which won’t give you full aid), why not Michigan?