We had been backing up all of our databases and image files to S3. Around 2TBs of data. But now we are migrating our hosting to amazon and I think we need another backup now, not on amazon. Is this correct? If so any recommendations? preferably an affordable, easy solution.
You could simply buy an unlimited space hosting account and run nightly backups to there with a scripted ftp client that pulls the backup down to your company's network each night - this is what I do, as it cheap and provides some redundancy against internal and external network/disk failure.
"Need" is hard to define. Hopefully Amazon will never lose your data, but of course they can't guarantee that. What you could do is back up to a different AWS region so that your backup is on a different continent to your live system.
Unlimited space hosting accounts are not always unlimited. From hostmonster.com's TOS
"Accounts with a large number of files (inode count in excess of 200,000) can have an adverse affect on server performance. Similarly, accounts with an excessive number of MySQL/PostgreSQL tables (i.e., in excess of 1000 database tables) or of database size (i.e., in excess of 3GB total MySQL/PostgreSQL usage or 2GB MySQL/PostgreSQL usage in a single database) negatively affect the performance of the server. HostMonster.com may request that the number of files/inodes, database tables, or total database usage be reduced to ensure proper performance or may terminate the Subscriber's account, with or without notice."
Once you go over 200,000 files you'll get an email and your account is suspended until you reduce your file count. Once you reduce the file count they'll unlock your account. I'm sure other "unlimited" hosts have similar policies.
You mentioned around 2 terabytes of data. I would contact them about their storage limit policies before hand and check your file counts before using an unlimited host for backups.
Smugmug.com uses S3 for backups and Zoosk.com uses S3 for storage. I would use the AWS calculator to figure out if it's the most affordable. But it's certainly the most reliable.