You have to choose either one of Bhutan and North East because North East itself requires at least 15 days to cover Arunachal, Meghalaya Assam (Excluding Nagaland). What you can do is, start from North Bengal that is Darjeeling then enter Sikkim and then Bhutan.
Covering the entire North east in 7 days is close to impossible. I would suggest you pick 2 states. You can fly to Bagdogra which is close to Gangtok. You can cover north Sikkim, Gangtok itself, Nathu La pass (which is sort of like the east of Sikkim) and Pelling (which is the west). Then you can go to Assam and cover kaziranga, pobitaro, majuli and Guwahati. From guwahati, you can go back to Delhi. Actually if you count it from one weekend to the next weekend, that's like 9 days. That is more than enough to cover 2 states including the commute, stay, etc.