You can visit mostly places with pet like Neel Garh waterfall short trek, Laxman Jhula, Neelkanth Temple. Also if you are going for Camping then it will.be great. Also don't miss the mexican food in Little Buddha Cafe .
Rishikesh is a good weekend gateway i must say.
u can book shivpuri resort along with your pet or if u like camping book jungle resort camp or beach camp on the banks of ganga river.both will allow pet animal .they all charge mini 1000/-per person including all meals.