Some of the places you wish to visit are quite far apart. It will require some extensive traveling. LA, Frisco and Vegas are all on the West Coast, but even they are hundreds of miles apart. Washington, New York and Pittsburgh are near the East Coast almost 3,000 miles (5,000 km) from LA. Dallas Texas is approximately half way between the two coasts.
If you are traveling from India, it might be wise to stop at the West Coast on your way to Pittsburgh or on your way home.
Clearly, the best way to go from coast to coast is by air. You can usually purchase round-trip tickets between LA and Pittsburgh, New York or Washington for about $300 if you reserve in advance.
From Pittsburgh you can typically purchase a round-trip airline ticket to New York for about $100. You can also buy a round trip airline ticket to Baltimore, near Washington DC, for about $100 on Southwest Airlines, a discount air carrier. Other than driving a car, air travel is the most convenient way to visit between Pittsburgh, New York and Washington. I suggest you plan on visiting New York and Washington during your stay in Pittsburgh by taking some inexpenive air flights to each city and spending a few days.
I live in Pittsburgh, and would be happy to meet you for a drink. Just contact me in advance of your visit.
On the West Coast, you can likewise find flight between Los Angeles and San Francisco or between Los Angeles and Las Vegas for about $100. That would be the most convenient and most economical way to travel between those cities. Unless you have some special reason to go to Dallas, I would save that visit until another trip, otherwise it will require a considerable detour and more extensive air travel.