Here are a couple links to check out:
HP 620 - New
I have ordered from NewEgg and I have had good experiences.
Here is another at TigerDirect :
Just don't get Asus confused with Acer, the difference is night and day.
Dell's consumer website has some computers that might fit their needs:
If you get a computer running Windows 7, I would suggest getting an external hard drive and making a backup image every couple of months. That way, when they bomb it with a virus, you can load from image and make your life easy.
Of course, if all they do is go online and do web-based e-mail, you could do what I did with my mom's computer.
I loaded Ubuntu on her machine and I haven't had to re-image her computer in 6 months. That makes me a happy guy.