I am sending emails to my salesforce contacts using marketing cloud. For this I import contact in SFMC and then send the email. Now when a contact clicks unsubscribe I want to set the Email opt out field to be changed to true in Salesforce back. I want to keep my data in sync. What are the other options if I don't want to use the Marketing Cloud connector.
If you use the Marketing Cloud Connector, this will be done automatically. You can simply send to a Salesforce Report.
Without Marketing Cloud Connector, there isn't a good option for syncing those back to the contact record. A custom app would need to be built that uses the Marketing Cloud and Sales Cloud APIs in order to pull the unsubscribes then update the Contact record on a regular basis to do the sync.
Another option would be to create a custom profile center/unsubscribe link so that at the time when the unsubscribe happens, separate API calls can be made to toggle the Subscriber in Marketing Cloud and Contact in Sales.