If you really want to party, I'd do something like this.

September: Austin City Limits in Austin, TX
October: Fantasy Fest in Key West, FL
November: Perhaps go to some college towns in the South and watch some key college football games in Baton Rouge, Gainesville, Austin, or other college towns. Spend Thanksgiving in New England for a traditional Thanksgiving meal.
December: Christmas and New Year's Eve in New York, New Year's at Times Square.
January: Sugar Bowl in New Orleans
February: Mardi Gras in New Orleans
March: Spring Break in (pick your city): S. Padre Island, Panama City, Lake Havasu City
April: French Quarter Fest in New Orleans, Jazz Fest in New Orleans
May: Jazz Fest in New Orleans, SF Carnaval
June: Chicago Blues Festival, numerous street festivals in NYC
July: 4th of July at either Boston or Washington DC, Milwaukee SummerFest, Taste of Chicago
August: Chicago Jazz Festival

The good thing about this itinerary is that you get to party hard, but you get to see some really amazing cities, like New York, Boston, Chicago, New Orleans, and San Francisco. You also get some Florida sun at Key West and for Spring Break.

Since you are most concerned about partying, I think you'd find this itinerary exciting.

If it's too much travel, you could pick cities around the seasons. For instance, New Orleans is great from January to May because of the many festivals, and Chicago is great from June to August. Just a suggestion.

Do you have a favorite band? Consider following them around the country on tour for the summer. Or meet up with some hippies and do the summer music fest circuit...lots of people spend their summer selling something at these festivals to pay for their way to the next festival.
Unless you love snow...stay south for the winter. A little vague, but to get you started: Fall in New England/Northeast, winter in the southern states and Cali, spring in Florida (spring break) and up the eastern coast and summer traveling across the northern states.
Some cities not to miss, besides the usual big ones (LA, NYC, Chicago, etc):
Portland, OR, Seattle, Nashville, Pittsburgh, Charlotte, NC, Lancaster, PA, Boston, Newport, RI, Delaware beaches, New Orleans, Savannah, GA, and Las Vegas (if you turn 21 while you're here), just to name a few!
Google US Road Trip...lots of things come up. Def check out www.roadsideamerica.com for some really wacky tourist attractions!
Have a blast! I'm so jealous!

You are only 20 years old. I remember when I was 20 (now 47) I will give you advice based on what you are likely to do wrong because you are young, and how to avoid it so that when you are 47 looking back you will not say "I see what I did wrong"
(The places to see a little farther down)

first problem:
Do not be short attention span-lazy, expect quick fix. You are off to a good start not doing that but I’ll mention it. Youth are likely to seek a quick fix itinerary, then go on the trip, then spend 20 years picking up bits of info here and there, resulting in the If I'd have known then what I know now, I would have done it differently. Doing this you are very likely to drive right past something never knowing it was there.

solution:
Put together a rough draft itinerary (easy) then research every town, region, State, attraction etc along that path. You will enter into a very enjoyable stage of discovery. "I did not know THAT was near by"
What I do is I print out every discovery that I like and put it in a plastic 3-ring binder pouch. it is easy to change the sequence of attractions. Some of these will be discarded as just not going to work out. Ultimately the itinerary just naturally comes together as if by divine appointment. This Fodors posting is a excellent start on the rough draft. Use the internet search engine for filling in the tiny details.

Second problem:
Youthful energy and the grass is greener around the bend. Too quick to move on.

Solution:
Realize you will probably NEVER pass that way again. Trust me the adventure is not around the next bend, it is happening where you are. Never leave and say I will see that next time. Unless fully willing to never see it. (a reasonable decision) Do your math, how many places do we need to see divided by 365, travel times etc. So that you are not frantically rushing about from poor planning.

Third problem:
Failing to plan for remembering. "time heals all wounds" time also diminishes the memory

Solution:
Take a lot of photos, and print them. Also keep a simple daily log. My daughter kept a simple daily list/log of our Canada tour. It is a family treasure of the memory sparking sort.

Seek out the only thing like it, the biggest, oldest etc.
Cedar Point Amusement Park Ohio, Mammoth cave, Kentucky Horse park, Old Louisville mansions., The Ringling Bros. Circus, San Francisco, The giant trees near San Fran, the only mobile historical landmark-San Fran Cable Cars, Monterey Bay Cal. National Marine Sanctuary,
Grand Canyon, Yellowstone, a fishing Charter on one of the Great Lakes, Mount Rushmore, Niagara Falls, The Corvette Plant tour Bowling green Kentucky. A Steamboat ride on the Mississippi, A rodeo somewhere in the west, Maine in October, The airport in Atlanta Georgia- Atlanta Hartsfield world's busiest airport, A Green Bay Packer football Game, A rural State Fair before they disappear forever, A chat with old timers sitting around some old small town downtown business, A sled dog ride in Michigan’s Upper peninsula, Walk some of the Appalachian trail in the Great Smoky Mountains. Take a coal mine tour, Watch a summer thunder boomer storm roll across the prairie, Tag along on a Noodling trip in Oklahoma.