Where are the cheapest places to stay on the East Coast of the US? ?

There are travel sites, even just maps you search, that will let you search for 'cheapest' this & that. Look OUTSIDE OF the major beaches and hot spots. It's a shame to give such advice though. I believe Cape Cod is not to be missed :D It is a peninsula of towns, each with this and that. Amazing vacation in the sun spot! You can even camp to stay cheap, in a forest near the beach. Get some saltwater taffy and a raft to float on, at a curio store! :D  Oh and the last town out is gay. :)

There really aren't any.  The best thing to do is stay in a place 20 miles from the beach. Any beach. 

If you're looking at total cost, then your travel expenses need to come into play so where you're coming from matters.  It also depends on what you're looking for.  A house on the beach?  A hotel 5 miles from the beach?  There are plenty of places in Florida to South Carolina where you can stay in a cheap motel 10 miles from the water.