I am a native of Nainital if you are in Nainital for 2 Nights and 3 days I would recommend you to stay a night in Nainital you can visit the famous Bhotia Market do not forget to try the Momos' they are super awesome a taxi booking can help you cover major attractions like snow view tiffin top....the next day you can plan to Pangot almost 16km from Nainital....here it could be more of relaxation and close to nature enjoying your leisure time...let me know what kind of a trip you are planning so that I can be more descriptive according to your need. for local food do try Anupam Restaurant they have recently added kumaoni cuisine to there menu. Apart from that I could also recommend you dining by the lake in Machaan the location is just awesome along with the food. Planning for a stay I would recommend you to explore options as there are many and then decide accordingly as it completely depends on your tastes and preferences let me know the details so that I can recommend you accordingly.
Pangot is hidden gem , you can explore bhotia market for shopping, for food sonam momos , chandi chowk restra their jalebi is so delicious, for non veg mezban machan is perfect