Yes in Rishikesh you can explore Nilkanth Temple... the path of this temple is very adventurous. This temple have a very interesting story related to Load Shiv....
other place to explore is Raja Ji National Park.. this park is famous for Elephants.
I think there are many campsite who can offer you to explore unkown places. You should contact them very first on the list is Patna waterfall. Half hour trek from Rishikesh but it is very beautiful trek.
Rishikesh is undoubtedly the best place for adventure seekers in India. Bungee jumping and Ganga river rafting is a must try in Rishikesh. Dev prayag and Haridwar is also near Rishikesh. Do not miss Jim Corbett national park if you have time as travel time from Rishikesh to Jim Corbett is comparatively longer.