Off the beaten track you can have a glimpse of the Ramgarhia bunga. It is a heritage building and one of the only puratan bungas left of the Sikh Misl Period. To access the place you can go behind the langar hall and ask a sewadar. The underground of the bunga really takes you back to the Misl Period with Nanakshahi bricks, niches to keep lamps for lighting and an old well untouched by the modern builders. It is advisable to take a torch there as it is dark.
Then you can go and meet Bhai Sahib Bhai Jeevan Singh ji. They live just behind Shree Akaal Takht Sahib ji. Its a wonderful experience
Also One would love to meet Bibi Amarjeet Kaur ji, the Singhni of Shaheed Bhai Fauja Singh ji, who just lives near Akaal Takht Sahib within the complex.
The Central Sikh Museum is a wonderful place to see in Amritsar Sahib. Among the famous artifacts it includes is a crystal vase which is an offering of Queen Elizabeth II, old poles which were used during the 1830's Gold Seva of Shree Harmandir Sahib, Old notice from 1850's asking Europeans to abide with Sikh rules when near to Amritsar, The shield used by Bhai Fauja Singh ji during 1978 Nirankari clash and much more...
The Company Bagh which is a little away from Amritsar Khas (takes about 15 minutes from Golden Temple when on a rickshaw). It is a wonderful yet not much known place. Company Bagh was the summer palace of Maharaja Ranjit Singh ji. Now it has a Maharaja Ranjit Singh Panorama Museum which exhibits wonderful displays from Maharaja's life. Also at the main gate of the Bagh one can see a Namdhari Shaheedi Asthan where the real Khalsa Kookas were hanged for killing the butchers of Amritsar.
If you would love to shop some Sarbloh bhande from Amritsar, don't buy them from the shops near to Harmandir Sahib for many of them are very costly and not real sarbloh (polished). There is a shop called Bhai Sohan Singh and sons in Lakshman Chowk, Amritsar (Near to Baba Deep Singh ji GURDWARA) that sells wonderful products made out of Sarbloh.
Hope this was helpful
Fateh to Guru Ram Dass ji's Charan
Dass
Harleen Singh