Your safest bet will be to stay in the Dharamshalas maintained by Sri Harimandir Sahib authorities.
Link 1 : http://www.goldentempleamritsar.org/accommodations-in-golden-temple-amritsar-accommodations-in-amritsar-sarai-booking-amritsar.php
Link 2 : http://sgpc.net/sarai-info/
If for any reason, you won't get any rooms here, worry not, there are plenty of budget hotels around Golden Temple only.
I stayed at Hotel Robin (booked through Booking.com) and it was a OK type of property. The best thing about the place - Its barely 2 mins walk to Jaliawala Bagh and 5 mins to Sri Harmandir Sahib.
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Please suggest him here in his thread:
At this time of the year it is difficult to get accommodation in the premises of Golden Temple.
What about food etc ?