Rishikesh is best for solo traveling and it's winter ryt now and I must say you must visit their, Rishikesh vibes different just pack you bags and go there well that's my opinion
Both Rishikesh and Haridwar can be covered in these two days, however my heart goes for Rishikesh. In Rishikesh you can easily spend two days in midst of the serene ganges river and lush green atmoshephere. Although Ganga Arti and temples are there but if you are looking for something different, then you can visit Beatles Asharm located at 1km away from lakshman jhula.. for lovely pictures and quaint surroundings. If you are a nature lover then you can also go to Rajaji National Park for jungle trails. Finishing your trip with the amazing ganga arti and food hopping at the cafes.
There's an amazing hidden village near Nainital, where not only you'll be able to see breathtaking views but you'll be flooded with beautiful clouds and mist. A quiet get away from the hustle and bustle of mainstream crowd. There are cafes eco homestaya in Pangot which are affordable and memorable indeed!
Rishikesh is best place to visit. Relax yourself by doing River rafting. Indulge in Yoga at mornings and end your day with some riverside cafe. Don't forget to taste the puchkas there. Ganga arti by ghats would be your takeaway from the trip.
There are places near nainital which you can explore but i would suggest you to plan haridwar since you can cover rishikesh and if time permits mussoorie too..