My brother and wife would like a 'not busy' type pattern for a quilt. Does anyone have any suggestions for a quilt that has a not busy pattern?

BQ3 is the pattern name. It is great and not busy if you use the right colors.
http://www.mapleislandquilts.com/quiltpatterns.asp

maybe just a 2 color quilt

Sometimes it's the choice of fabrics that makes it busy, not the pattern.

When I think of quilts that are not busy quilts that have a good amount of white. I think it helps to focus on the patterned fabrics but gives the eye a nice place to rest.

What is their style? More traditional or contemporary?

Their style is more contemporary. Yes, one with a lot of white would be the ticket. They liked a pattern called Spider Web, but it had a bazillion little flying geese. Too many for my patience level.

How about a snowball block? You could use different fabrics for the ball and white for the corners.

I love this pattern
http://www.ericas.com/quilting/patterns/39955b.jpg
and this one
http://www.rjrfabrics.com/patterns/d...n.cfm?psID=422

or what about something like this, there have been some gorgeous ones posted her on the board

http://www.quiltingboard.com/t-111021-1.htm

Why not a double or single Irish chain? That's striking, and you can use a lot of white.

What about some of Denyse Schmidt's patterns? Sometimes they can be a little bit fiddley, but not in the same way a ton of flying geese would be. I did "What a Bunch of Squares" for my SIL. The thing I like about her patterns is you can customize them to be as complex or simple as you want them to be.