Being home to the sacred River Ganga (Ganges), Uttarakhand is a very spiritual place.
The most significant temple around is the Neelkanth temple, and for most pilgrims that's the reason why they pass through Rishikesh. The nearest Jyotirling i'm aware of is in Kedarnath.
Har-ki-Pairi (God’s footprint) lies on a ghat of Holy River Ganga. The footprint belongs to one of the three main gods of Hinduism, Vishnu who is said to have spilled divine nectar at the spot. Worshippers come here every evening to wash away sins in the waters of Ganga. There is much faith about Har-ki-Pairi and it’s a major Hindu pilgrimage site. I don’t know how many sins get washed and how many remain, yet the footprint etched in the rock forever as a reminder of its sacred beginnings, draws deep faith of the Hindus.
Swarg Niwas Temple (Heaven Abode Temple)
“Keep on climbing the stairs n watching gods n goddesses, cos at the top u wl find yourself in heaven. From the top you can see the mountains around. A beautiful view”,* remarked a traveller trying to explain to experience of Swarg Niwas (Meaning: Heaven Abode)Temple. This twin-tower temple on the left bank of Lakshman Jhula houses a scattering of Hindu gods, goddesses and demi gods.
Shri Trayanbakshwar Temple, Rishikesh
Trayanbakshwar; literal meaning Abode of the three eyed, indicating Lord Shiv. The unique 13 storey shrine temple in Laxman Jhula is filled with plentiful Hindu deities, and lots of Vedic and religious works. A very prominent Hindu temple, Trayanbakshwar is said to be one of 12 Jyotirlings (Jyoti: Radience; Ling: The sacred phallus of Shiv) of Shiv.
Another reason for pilgrims to pass through the area is, of course, the Char Dham (more correctly Chota Char Dham): Gangotri, Yamunotri, Badrinath, Kedarnath.
Then there's a few more "minor" holy spots along the way, such as Rudraprayag, Devprayag (/Deoprayag) and Uttarkashi.
* Citation: Wild_punit: Tripadvisor.in/Attraction_Review-g580106-d3705590-Reviews-Swarg_Niwas_Temple-rishikesh_Uttarakhand.html