You could buy US Treasury bonds with the amount you do not need to keep liquid.
If I were you, I would keep 12 months in the highest paying combination of laddered FDIC-insured certificates of deposit (CD) I could find. Bankrate among other places will give you current CD rates.
http://www.bankrate.com/funnel/cd-investments/cd-investment-results.aspx?ic_id=CDI_compare_rates_module:www.bankrate.com:1_Yr_CD&local=false&prods=15 (Full disclosure: my own emergency fund is mostly in a savings account, because my credit union's savings account interest rate is higher than the new CDs are offering.) If you don't understand how a CD works, please ask. I'd mentally consider only that 12 months worth of expenses as my Emergency Fund Savings.
The rest I would mentally categorize as Investment. I'd decide what purpose I wanted to invest the money for. Retirement is the most popular one, but Financial Independence is probably the more common goal around here. Once you pick the goal, you choose how to invest. There are tax advantaged methods for the Retirement goal you have probably heard of: Roth IRA, Traditional IRA, 401k, and so on.
For most people a good way to go is this:
(1) Live below your means. (most likely a check for you)
(2) Save at least a 3 month Emergency Fund. (check)
(3) Pay off loans with high interest rates. [Definition of high varies.]
(4) Invest in available tax advantaged retirement accounts up to the legal maximum.
Are you looking for investment suggestions?