It seems you'd be able to pull it off, but it'd definitely be extra hassle and you might be subject to extra scrutiny (not to mention the cultural tensions between the two nations).
The Pakistani government says about tourist visas: "A non-extendable tourist visa valid for 14 days is issued by Pakistan High Commission, New Delhi through approved tour operators/travel agents." Depending on how strict they are about you visiting, you might have to get one of those through a travel agency. However, if you can slide by with a visitor's visa, you should have less trouble: "Visitors visa are issued to Indian Nationals to meet relatives, friends or for any other legitimate purpose. This type of visa is also issued to bonafide Indian businessmen for six months with three entries."
In addition, it seems you can only enter/exit through certain areas as an Indian national:
Following are the designated entry/exit check posts for Indian
nationals, coming to Pakistan:-
i By Air Karachi/Lahore/Islamabad.
ii By Sea Karachi.
iii By Road Wagha.
The Pakistani government actually has a tourism website for the region and they talk about visa requirements. They seem to be the same as the rest of Pakistan—except for India (and Israel).
The Pakistan Missions abroad are authorized to issue tourist visa for
a maximum period of three months liberally to all foreign nationals
except to the Indian nationals and the foreigners of Indian origin and
the nationals of Israel. All foreign nationals, including tourists,
are exempted from police registration, except the nationals from
negative list countries.
So it looks like you might have to deal with some form of police registration or extra scrutiny. Nowhere, though, does it say that Indian citizens are denied entry to the region.
I wasn't able to find much information on rules / visiting, even though they have a tourism website. The only thing I was able to find from the actual government site:
Tourist from all parts of the State of Pakistan can visit Azad Jammu
& Kashmir without any restriction. However, they are advised to keep
their identity with them. Foreign tourists can visit Azad Kashmir
except the areas situated within 16 kilometers along the Line of
Control (LoC). Before planning their visit foreigners should contact
Interior Ministry Government of Pakistan Islamabad for issuance of
NOC before visiting Azad Kashmir.
A NOC is a no objection certificate—basically a letter from the government saying that "we're fine with so and so doing X, Y, and Z". I'd read over this thread from the Lonely Planet forums and this page (PDF warning) from the Lonely Planet Pakistan guidebook on getting NOCs and travelling in the area. They don't explicitly mention Indian citizens (I have a feeling the tensions between the states would make getting an NOC harder, especially if you want to travel alone without a travel agency) though.