If you guys love adventures then you can go for Haridwar and Rishikesh. Try Bunjee Jumping. It'll be a memorable experience for you. Cost will be 3500 per head. You can also try Flying Fox..combo cost will be 5000 per head. Take Jana-Satabdi from Delhi to Haridwar. Stayed at Haridwar. book hotels via MMT.
Upper & lower Dharamshala, Palampur, Danaulti, Kasauli, Chandigarh, Jaipur, Mumbai (for lesser days via train) Bhopal, Gwalior, Lucknow, Varanasi, Chopta, Lansdowne, many more although many places may be hot in peak afternoon hours.
Under 16000, is a rather tough budget to match but I guess it is adequate to visit any place in Himachal Pradesh. the lush greenery is always welcoming and with the winters behind you, the centers are bursting with new fresh energy. I highly recommend Somapura, which is 2km from Kasol, right next to the forest and on the banks of river Parvati. it is a perfect place to have a peaceful bornfire in the forest with your special someone, especially if you are able to mix wine into the sittuation. this place also has lots of beautiful cottages to choose with excellent amenities and pocket friendly package s