Ans :- Danger and risk are relative. I have lived in Nainital for a few years and can tell you atleast this much:

It rains a lot in Nainital due to its geography. I have lived in other hill stations as well (currently Manali) but, Nainital has one of the wildest monsoons in Uttaranchal/Himachal combined.

Last year a cloud burst over the city, resulted in several landslides within the city as well as water logging washed away some buildings including a major chunk of a popular hotel on the mall and a restaurant as well. These sites and a few cars were buried under the silt when the water ran into the lake. I guess one/two people were killed (not sure though about this part). I lost a phone and a laptop due to the rain :/

Unauthorised construction on the mall side of the city, results in these landslides and water logging. So good luck if your hotel room is constructed on landslide zone or blocks a designated water channel.

Nainital is otherwise a very beautiful place. One of my favorites until now. Loved it even through the rain clouds and especially enjoyed going swimming around that time of the year.