I want to travel outside of the east coast eventually, but can't because of financial reasons? How do I plan an inexpensive vacation?

You have travelled only along the east coast.

You plan a trip of hundred miles they same way you do one of a thousand or five thousand.
ONE DAY at a time.
The basics transportation,food, a place to sleep. Stuff to see and do.

As you have not said where on the east coast you are starting not easy to give much direction.

Depending on the budget. You can go for a weekend a week a month. For example when there is a seat sale on an Airline you can get to and from far away place. Your time at that place depends on your budget.

There is much more to the country than just some big city or the expensive amusement park. It really depends on what you want to do and see on your adventure. Many free town festivals. Check local event guides for a time you might be there. County Fairs,State fairs. You can stay in a tent, a low cost motel/hotel.

Meals DO NOT have to be in restaurants all the time. A stop at the grocery store and a simple cooler and you can get stuff to make meals for the family at the side of the road or your room for the night.

https://www.allegiantair.com/
https://www.flyporter.com/Flight?culture=en-CA


OUT WEST can you narrow this down a little half the country is WEST of the Mississippi you will never see it all.

Try these Airlines see which ones have something from where you live,
AirTran -USA
Flights from many cities in the Eastern USA
Allegiant Air -USA
Flights between Las Vegas and several East Coast cities
Frontier Airlines -USA
Flights from Denver (major hub) to many US destinations
Horizon Air -USA
Flights within the USA and from the USA to Canada, Mexico
JetBlue Airways -USA
Flights within the USA and from the USA to the Caribbean, Central America
Midwest Express -USA
Flights within the USA
Southwest Airlines -USA
Flights within the USA
Spirit Airlines -USA
Flights within the USA (major hub Fort Lauderdale) and from the USA to the Caribbean, Central America, South America
Sun Country Airlines -USA
Flights within the USA (major hub Minneapolis) and from the USA to Mexico, U.K.
Sunwing Airlines -Canada
Flights within Canada and from Canada to USA, Mexico, Central America, Caribbean
USA 3000 Airlines -USA
Flights from Midwest and Northeastern USA to Florida, Cancun, Dom.Rep.
Virgin America -USA
Flights within the USA
Westjet -Canada
Flights within Canada and from Canada to the USA, Caribbean

At your destination you do not have to rent a car. Many day tours available to take you to the sights. Or use local transit to explore. Most have a day pass for unlimited on and off rides. Maybe you just WALK

Lower prices are when you do your big travel Tuesdays Wednesdays and Thursdays.

If someone in the family is an AAA member you can get free travel guides and maps to plan an adventure. They will even help with that once you have an idea of where you want to go and your budget and time.

For budget purposes. A driving trip about $0.50 per mile. Google map can help you with the distance.

$100/night place to sleep can be much more. Food for 5 $100/day will be more if you eat in restaurants every meal.

Entrance charge to something along the way . Budget at least $100 You can look up specific prices.

State parks usually very cheap day. Want to see the Mountains you can to that in Boise cheaper.
Want to see the west Coast Ocean cheaper in Portland/ Want to go the Southern California? Burbank cheaper than LAX.

Start with ONE place find out how to get there. What there is to do there for your budget. If you have a bigger budget you add on additional places in far away state.

Your exact budget will depend on where you go, how you get there and what you do when you are there.
The numbers above are just to get you started.
Remember many places have FREE and low cost things to do as well as the expensive things.

As you and your siblings are students. Try some STUDENT travel sites for ideas. Many discounts for Students.

Campgrounds and small car. Just did a 3600 mile ski trip for a couple hundred bucks.

Figure out what your budget is, then work backwards.

well, is one of your siblings dying? contact Make-A-Wish

Use Travelocity or any similar site to find out the cost of hotels. Find out what mileage your car gets and the cost of gas. In other words do some planning that your education should have prepared you to do.

The first thing to do is sort out your budget.

Do you have a part-time job? If so, you can save up for the trip.