Places you can visit near Rishikesh and Haridwaar are Mussoorie, Kuari Pass, Dehradun, Chakrata, Corbett National Park, Tehri Garhwal, Chamba, Dhanaulti, Lansdowne and Nainital.
If you are in rishikesh you must visit neer waterfalls it is very peace giving. You can go to Dehradun there are many things to do. You can visit Tapkeshwar Temple, Guchhupani, Sahasradhara and Tiger Falls is the must visit place near Dehradun. If you have extra day you can also go to Mussoorie and Dhanaulti.
Places to visit near Haridwar: Dehradun Mussoorie Kanatal Lansdowne Sattal Auli Kasauli Some places are far away but still it will give you the most awesome feeling and adventure if you are planning for outing then I suggest you to go to Auli.. Best place of attraction Nainital.
Rishikesh, lot of places are there with sports activity also like rafting , bunjee jumping and Neel garh waterfall and Neel.kanth temple.
Also can go Dehradun, Massoorie, Dhanaulti.
You can go to following places:
Dehradun (60km from haridwar)
Massoori (36k. From dehradun)..... Inhere u cn to popular kempty waterfall.
Then kanatal (80 km rishikesh)
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Haridwar - हरी की पौड़ी,माँ मनसा देवी मन्दिर, चंडी देवी मन्दिर, माया देवी मन्दिर , सप्तऋषि आश्रम , भारत माता मन्दिर , माता वैष्णो देवी गुफ़ा मन्दिर (माता लाल देवी मन्दिर ) , भूमा निकेतन , तुलसी मानस मन्दिर ( श्रीराम मन्दिर ) , शिवानन्द धाम , इण्डिया टेम्पल , पावन धाम / कांच का मन्दिर / शीश महल , दक्ष महादेव मन्दिर , हरिहर आश्रम ( पारद शिवलिंग और रुद्राक्ष का पेड़ ) , पायलट बाबा आश्रम , शान्तिकुंज