I know I can Connect to any web service from visual web part.

I can write C# code behind to get data from the service and display it in server controls.

My question to the 365 team is; can I do it in a sandbox solution deployed to 365 (2010 version)

Thanks

You can't call a web service from the server side code of a sandbox solution.  There's a good explanation in this thread.

http://social.technet.microsoft.com/Forums/en-US/462be803-eea5-4bdd-ad18-c774d94c8fa9/external-web-service-call-from-sandbox-solution-in-sharepoint-2010

You can however deploy client side code in a sandbox solution that will call a web service.