Most airlines have the policy that you can't travel within 30 days of your due date domestically, and withing 60 days of your due date internationally. So you should be okay upto 32 weeks.
I flew at 20 weeks, and other than a nasty cold that I picked up on the plane it was good. I didn't necessarily look pregnant yet either, just like I was carrying a few extra pounds so I never even got asked any questions. Getting a seat where you can use the bathroom often without climbing over people is a very good idea, even if you don't usually sit on the aisle.