Traveling when you're young is the best time. You are full of life and need to explore the world outside of home.
1. New York City
This is slightly overrated if you go to the city and spend the majority of your time in Times Square and take an uber everywhere. If you live like a local and try to avoid the tourist spots, you will absorb so much more of the culture.
The parks are free and beautifully urban. Taking the subway will save you money in the long run and will make you feel like a native New Yorker. Skip the expensive boat tours of the Statue of Liberty and take the Staten Island Ferry for free, it goes right past the statue. New York City is one of the epicenters of culture so skip shopping and go to a museum!
2. Washington D.C.
The capital of the greatest country. D.C. is rich with history. It's like you can almost absorb a history lesson. This city is much, much cleaner than New York, but is equally as beautiful. D.C. is expensive, yes, but there are so many things you can do for free, which is great for everyone because we are all broke.
You can visit the monuments and museums, there are definitely plenty of both. You can even visit the back of the White House where there are always protests going on. There is even a tent that is a protest and has to have someone in it 24/7!
3. Pittsburgh PA
Pittsburgh will always has a special place in my heart since it is the closest big city to my childhood home. One of the best feelings is coming out of Liberty Tunnel and seeing the skyline or going to the overlook at night. Catch a Pirates game in the summer or a Penguins game in the late winter. Pittsburgh is a city to have a relaxing yet exciting weekend.
These are just some of the cities I hold close to my heart. If you get a chance, visit them. You're only young once, explore and visit everywhere you can before you settle down with a family.