The nearest Domestic Airport from Nainital is Pantnagar Airport,

Overnight air-conditioned train from Old Delhi railway station (departing at 2235 hr.) to Kathgodam (arriving
at 0615 hr.) and then 2 hr. drive to Pangot via Nainital.

Overnight air-conditioned train from Old Delhi railway station (departing at 2235 hr.) to Ramnagar (arriving at
0500 hr.) and then 2½ hr. drive to Pangot via Kaladungi.

There are now day trains to Kathgodam and Ramnagar as well.

To get to Pangot, one can take any of the following options:
Google Maps 29.423152, 79.426421

Drive from Delhi via Kathgodam and Nainital: 8 hours

Drive from Delhi via Ramnagar (Corbett National Park) and Kaladungi: 7½ hours