Only show widget to contributor role

yep, that should work. But levels are on their way out. officially ‘deprecated’ meaning support will be dropped in a future WP release. I think the recommended way would be to use capabilities like

current_user_can('edit_posts')

which normally is true for contributors, authors, editors, admins etc. If you want to be specific you could tie it down to just contributors with

current_user_can('edit_posts') && !current_user_can('edit_published_posts')

Alternatively you could use this non-standard function appthemes_check_user_role() to check by named role
http://docs.appthemes.com/tutorials/wordpress-check-user-role-function/

Hope that helps

http://codex.wordpress.org/Roles_and_Capabilities#Contributor