The easiest way to think about possible investments is in terms of risk and return.
1. Mortgage
Paying off your mortgage is an 'investment' that will provide a 'guaranteed' (low risk) return of the APR of the mortgage, less the amount you receive as a tax deduction from your mortgage interest.
2. Treasuries
Buying treasury bonds or notes (see TreasuryDirect.gov) will also provide money that is also low risk (the government can always print more money if they need to) but as you will see, the rates of return are amongst the lowest, even taking into account that they are not subject to state tax. If you are offered lower returns than that (e.g. by your bank), you would be better off putting your money in treasuries (taking into account ease of accessing the money).
3. Other Asset Classes
Putting money in higher risk asset classes may provide more of a return, but they can be subject to the swings in the market. It can also be time consuming learning about the market and keeping up. The general rule is the more return an asset provides, the more risky it is to invest in.
Diversification
You can also benefit from diversification. If you put your money evenly across 5 different stocks, rather than one, if one goes bankrupt, you haven't lost all of your money.
Personal Situation
Given the information you provided, it is difficult to determine what is appropriate for your situation. Most brokers are legally required to ensure that any recommendations they make are suitable before making them, so would require more detailed information about your situation.
Independent Quality Advice
If you want to get started with investments, pick up some books on investing from your local library. You might want to start looking into index tracking funds, such as the ones that follow the S&P 500, and if you are interested in specific companies, research those as well.
Conclusion
Keep in mind, you may find that the best investment is to pay off your mortgage, but it is worth considering alternatives, particularly from a diversification standpoint - if all of your money is invested in your home and you need to move and the housing market has dropped, you could be in a difficult situation.
