Yes, you'll find most hotel room reservations are fully refundable if cancelled before the hotel's cancellation deadline, which in most cases is within 24 or 48 hours of your check-in date. If your reservation is non-refundable, it might still be possible to cancel it and get a refund within 24 hours of booking. Add your dates and click on "Search", then use the "fully refundable" filter to review the best deals near Mongar Dzong.
