You sure he didn't say cv joint or drive axle bec it does sound like that is the problem or a wheel bearing and I get more then one opinion on it , some shops offer free estimates and be sure that they actually show you and explain what is faulty on it.
It being a U joint doesn't quite make sense from what you say the vehicle is doing and when its doing it but it could be the cause too.
If you look inside behind the wheel as the front wheel is turned you'll see a shaft with a accordion like plastic or rubber piece and if you see that its clamps are loose or its bulged or damaged etc that tell you if the outer cv joint is bad especially if the boot is damaged.
Hope that helps and best of luck.By the way again be sure you get a few opinions and quotes and maybe if you can buy the parts yourself you might be able to save some cash and also arrange a flat rate labor price on the work too but be sure you get a warranty on parts and work.
