Depending on age, a Hello Kitty would be appropriate. Just be aware there is a smaller, cheaper version that is more of a toy. The larger one would be much better. (about $110)
http://www.target.com/gp/detail.html...roogle_df&LNM=|
If you don't want the Hello Kitty logo (a more grownup machine), similar machines are available in the Janome Jem line.
http://www.sewvacdirect.com/janome660jem.html
The "Hello Kitty" and probably Kenmore-branded versions of the Janome are also available from Sears.
http://www.sears.com/shc/s/p_10153_1...tcmp=ST_Sewing
The advantages of these machines are that they are real machines that work well but they're 3/4 size, lightweight, and portable. Toy machines just frustrate children. These are the real deal. (Even work as machines quilters carry to classes.)
Also check eBay and Overstock.com . eBay might have some of the older Janome Jem models available new for less $$$.
Edit: I see others have recommended a full-size machine. I still think a 3/4-size is more appropriate for an 11yo plus, if you already have a full-size machine in your house, a lightweight 3/4-size is nice to have for taking to classes (or for your 11yo to take to classes). Just my 2 cents.....