For some ideas on investing priority guidelines, see Oversimplify it for me: the correct order of investing.
Congratulations on being debt free! My advice to you is to do what you can to remain debt free.
You could certainly invest the money; it will earn much more over the long-term in a stock mutual fund than it would left in a savings account. However, if you need any of this money in the next few years, it would be a shame if it lost money in the short-term.
How much do you need to finish grad school? Don't invest that money in the stock market, because you will need it over the next few years.
Likewise, think about other expenses that are coming up. Will your car need to be replaced in the next couple of years? Will you have enough income to meet your living expenses while you are in grad school, or will you need some of this to money to help with that?
Finally, it would be good to keep some extra as an emergency fund, so you can easily pay for any unexpected expenses that come up.
If you can make it through grad school debt free, you will be much better off than if you invest all the money but take out student loans in the process.
After you've accounted for all of that, whatever is left of the money could definitely be invested. If your goal is to start a retirement fund, an index mutual fund invested inside a Roth IRA is a great place to start.