Parihaspora
Visit the ruins located on the outskirts of Srinagar on way to Gulmarg. See the palaces of Kahmir's Buddhist and Hindu rulers and Buddhist places of worship.
All the hotels organize excursions 1, 2, 4 days to see the Himalayan mountains. Beside that package tours by JKTDC can be a good option. Using an honest guide or fixer can potentially save you money on goods and accomodation.
Go for a Shikara ride in the Dal lake which costs around Rs 150 off season - Rs 500 peak season for the whole Shikara. For better views and a more peaceful ride in an area devoid of other tourists, walk up a fair bit of distance till you can see the fountain and ask the Shikara rider to take you for a ride to the fountain. It costs Rs 300 off season - Rs 600 peak season. Make sure you bargain a little, especially in off season. If you are staying longer, you could go on shikara rides more than once... each time to a different part of the lake. A must see is the "village" in the lake. Ask for a ride to the side where locals live and see the floating vegetable market. The market is usually operational only at sunrise and is easiest organised through an agent or your hotel/houseboat.