Although Michelle Williams still plans on spending more time in LA, she has been looking at Brooklyn properties ever since she put the Boerum Hill home she once shared with her late partner Heath Ledger, on the market for $7.5 million in September — far more than the $3.6 million they paid in 2005.

Our spies have spotted Williams checking out less grand homes in Bedford-Stuyvesant and Fort Greene — far from the cushy comfort of Boerum Hill.

“I was shocked to see her,” one spy said. “She was looking at everything on the market, high and low — probably because there isn’t much inventory.”