First off, good on you for taking financial responsibility. Once you're out of school, priority #1 is setting up a rainy day fund. You need enough liquid cash to survive a minimum of three to six months without a job.
If you are willing to work in an area with a severe healthcare shortage for a period of two to three years, the Nurse Corps program will pay off either 60 or 85% of your loan. You need at least a 100% debt-to-salary ratio to be considered a Tier 1 candidate. This means that if you're expected to make less than $50,000 your first year, you have over a 100% ratio; this will probably be mostly determined by where you live and what RN starting salaries are.
If your debt is through the feds, you qualify for Public Service Loan Forgiveness provided that you work full-time for a non-profit. This means you make payments on your loans for a period of 10 years, and your remaining balance is forgiven. There are three major risks to PSLF.
1) Income. If you make around $40,000 or $50,000 and you opt into REPAYE or one of the other 10% income-dependent payment plans, you'll only wind up paying about $20,000 or $25,000 before the escape hatch kicks in. If you live in an area of the country such as California where starting salaries for RNs are high, your monthly payments will be quite high, and the loan will probably be paid off before you reach the 10 year mark.
2) Fewer opportunities. While most hospitals are nonprofits, if you want to take an offer in the private sector (say, an informatics job at one of the EHR companies or a doctor's office), too bad, you can't.
3) The government factor. No one has actually had their loan balance discharged through PSLF yet; the first people are set to call in their forgiveness this year. There's nothing that says .gov can't change the program or walk back their side of the deal.
If neither of these programs sound like a good idea and you do want to go the payoff route, try refinancing through SoFi, Earnest, or another borrower to lower your interest rates so that more of your payment goes to principal. Pay off the highest interest loan first; it's a better return on investment.