I have visit there twice. You don't have to get visa. But you have to get a pass there by showing your Indian Identity Pass. If you want to visit Phuntsholing, there will be no problem but after that you need pass. Happy travel!
No visa for Bhutan and Nepal.
For Bhutan, you need to get a permit which can be obtained from phuentsholing. It is the only place in Bhutan where one does not need any permit. Office is closed on Nepal National Holiday days(which can be checked on net). Permit for entry in rest of Bhutan can't be obtained on these days.
Nearest Indian town is Jaigaon (30 min) ride
Nearest airport is bagdogra (3-4 hrs drive)
Nearest railway station is Hasimara (2-3 hrs drive)
Have passport or Voter id, best for quick permit
Visa is not required, just keep your identity proofs, aadhar and voter id, you may keep your passport for safe-side. The best place to visit nepal is Pokhara, but do visit kathmandu also. Best weather will be August to November.
all the best.