Federal travelers’ lodging per diems will decline in 310 areas — some quite sharply — beginning in October, as we reported yesterday. Headed to Manhattan next May? You’ll have $106 less to spend on a hotel each day than you would have a year earlier. Chicago in June? Per diems are scheduled to drop from $211 to $166. It’s not entirely unexpected. The recession has hit the travel industry hard, and hotels across the nation have dropped their rates in recent years to encourage travelers. They’ve also become more willing to work with the federal government. We’d like to hear…