As I begin to accelerate a humming sound from the front of the car begins. The noise becomes more pronounced the faster I go. No additional noise is made when I brake or turn, nor does it appear to be any noise when I went in reverse. I made a 180 mile trip on Sunday with no problems, although I did travel at closer to 55mph than 65. The car has 170,000 miles on it and has had most of its scheduled maintaince performed.
You need to describe the sound better. From what you’ve said it could be anything from transmission whine (normal) to an angry badger telling you to slow down 
Does it sound as though you are driving on rumble strips? You could have one or more hub assemblies (wheel bearings) going bad. These are common on these cars as they age.
The noise sounds like the transmissiion is stuck in low gear and prgressively gets louder and more distinct the faster I go. I also thought maybe it was coming from the engine, but I have no clue as to what that would be It’s not the noise I would associate with a transmission low on fluid. I was going 55 on Sunday and put it in neutral; the noise kept going. The tires are good ones and have about25-30,000 miles on them. As I mentioned, I did try backing up at about 15-20 miles an hour and i didn’t hear any noise then. Any thoughts you might have would be helpful and appreciated: 2000 Buick LeSabre Limited; 177,000 miles.