When it comes figuring out how they'll pay for college, many families start by shying away from pricey private schools.

Yes, annual tuition plus room and board at four-year, private universities is much higher — $48,510, on average in the current academic year — compared with just $21,370 at public institutions, according to the College Board.

However, about two-thirds of all full-time students receive aid, which can bring the net price way down.

Your net price is a college's tuition and fees minus grants, scholarships and education tax benefits, according to the College Board.

In fact, the top schools for financial aid all have sky-high sticker prices, yet their very generous aid packages make them surprisingly affordable, according to The Princeton Review.

"Don't make the tragic mistake of crossing an expensive school off your list of consideration," said Robert Franek, The Princeton Review's editor-in-chief and author of "The Best Value Colleges."

WATCH: Why college is so expensive

When it comes to offering aid, private schools typically have more money to spend, he added. In fact, "these schools become even more affordable than your home state university."

The Princeton Review ranked colleges by how much financial aid is awarded and how satisfied students are with their packages. The report is based on data collected from fall 2017 through summer 2018.

Here are the top 10:

Location: Hamilton, New York
Tuition, fees, room and board: $67,500
Average need-based scholarship: $48,369
Out-of-pocket cost: $19,131

Students here have a healthy dose of school spirit, with good reason: Colgate is one of the top liberal arts schools in the country, even though it has a price tag to match. Still, students receive over $48,000 in grant aid, on average, making it a much more affordable place to matriculate.

Location: Pasadena, California
Tuition, fees, room and board: $64,704
Average need-based scholarship: $45,797
Out-of-pocket cost: $18,907

This small school in the mountains near Los Angeles is a worldwide academic powerhouse. The science and engineering college boasts a lengthy history of significant research achievements and it also delivers on aid, meeting 100 percent of demonstrated student need.

Location: St. Louis, Missouri
Tuition, fees, room and board: $69,839
Average need-based scholarship: $43,745
Out-of-pocket cost: $26,094

At first glance, Wash U. is another one of the pricier schools on The Princeton Review list. However, it is similarly committed to helping defray the cost without relying on loan debt. For starters, it has eliminated need-based loans to students from low- and middle-income families, which means that those dollars never have to be paid back.

Location: Williamstown, Massachusetts
Tuition, fees, room and board: $69,950
Average need-based scholarship: $51,773
Out-of-pocket cost: $18,177

One of the nation's very best schools – on par with any Ivy league institution — Williams College also gets a top score for its ability to finance its students' educations. The school meets 100 percent of demonstrated need for all undergrads for all four years. "You'd be insane to choose a lesser school instead because of the sticker price," Franek said.

Location: Nashville, Tennessee
Tuition, fees, room and board: $66,050
Average need-based scholarship: $47,294
Out-of-pocket cost: $18,756

Every year, Vanderbilt distributes more than $42 million in aid. In addition to gift assistance, the school is known for its three signature scholarships, which all cover full tuition and offer summer stipends to study abroad, complete service projects or conduct research. And they are renewable for all four years of college.

Location: Claremont, California
Tuition, fees, room and board: $67,225
Average need-based scholarship: $50,069
Out-of-pocket cost: $17,156

As a member of the Claremont Colleges, a group of highly regarded schools just outside of Los Angeles, admission to Pomona is tough but also need-blind. The goal is to achieve "significant socio-economic diversity," according to Adam Sapp, Pomona's senior associate dean and director of admissions.

Location: New Haven, Connecticut
Tuition, fees, room and board: $64,650
Average need-based scholarship: $47,960
Out-of-pocket cost: $16,690

This Ivy puts its money where its mouth is: Committed to meeting 100 percent of each applicant's demonstrated need, Yale spends more than $140 million on financial aid each year. As a result, more than 10 percent of the student body will have $0 expected parent contribution in 2019.

Location: Princeton, New Jersey
Tuition, fees, room and board: $62,750
Average need-based scholarship: $51,365
Out-of-pocket cost: $11,385

This is another elite Ivy League school that makes the top of many college lists. It's also highly regarded for its war on student debt. Princeton has eliminated all loans for students who qualify for aid. Instead, awards come in the form of grants that do not need to be repaid.

Location: Poughkeepsie, New York
Tuition, fees, room and board: $70,510
Average need-based scholarship: $48,194
Out-of-pocket cost: $22,316

Vassar is one of most expensive colleges in the country and also one of the most generous. The average scholarship is just over $48,000, making this top liberal arts school with a stunning campus harder to get into than afford.