For fall travel, fly from Houston to Rome for $455 round-trip on American. Dates are available over the Thanksgiving holiday.
For example, I found seats departing Houston IAH on Wednesday, November 21, returning from Rome FCO on Saturday, December 1.
You'll find other dates available for travel in November/December. A 7-night minimum stay is required.
Time is running out to get low fares like this including one free checked bag. American plans to introduce basic economy fares to Europe soon and the low fares will likely not include any checked bags in the future. For now, I'm still only seeing regular economy fares on European routes.
Need a room in Rome? Here's what's available for the above dates on Hotelwatchdog.