I have used priceline.com and have not had a good experience. While it is true that they will not give you times you can presume it is pretty much the crappiest flight of the day (read: red-eye).

When I went I had a couple of issues:
1 - they will not give frequent flyer miles. OK, not a problem for me, I gots plenty.

2 - they will not allow you to change your flight. This was an issue. I wanted to come home early from a conference and could not.

3 - They will not allow the airlines to change your flight. This is the killer. I was flying from LAS to PHL through cincinatti and would have had a 3 hour layover. There was a flight on the same airlines DIRECT that would have gotten in 4 hours earlier and there were plenty of seats. The airlines would not change it as per the agreement with priceline.

I will not use them again.