Don't give up on your money market fund.
We hold money market funds for a variety of reasons. They can be an emergency backup should we lose our job or have uninsured damage to our house (or to ourselves). They can be a spot to park your money while you wait for a new opportunity to present itself.
They are also a good place to put money that you intend to spend on a big-ticket item like a car or tuition in the next two years. Finally, some investors own them just to have a superlow-risk portion in their portfolio that can reduce the pain of a year like 2008 and provide dry powder to put to work in a sell off.
But today, many money market funds are yielding just 0.01%, and some investors are rushing to short-term-bond funds and ultrashort-bond funds in order to get some income. Many fund companies have been forced to eat some or all of their expense ratios in order to keep yields from going to zero. It's not a fund-company conspiracy--Treasury bills just have incredibly low yields.
We're still wary of ultrashort funds. Short-term bond funds can work if some losses in the short run are acceptable--for example, if you are parking money between investments, plan to hold for a year or two, or just want a conservative bond holding in your long-term asset-allocation scheme. Consider Vanguard Short-Term Bond Index
But for other uses, such as emergencies or upcoming big-ticket expenditures, I'd stay with money market funds. Think about what will happen when interest rates start to rise. Bond funds will initially lose money because their superlow-yielding bonds will be discounted in the face of new higher-paying bonds. On the other hand, money market funds will quickly start to have higher yields, yet they won't lose money when rates go back up.
Bank accounts are another decent alternative--though their yields aren't much better--if you have less than $250,000 (the FDIC insurance limit) to put in a bank account and can get a decent yield without committing to a long-term CD. However, above that insurance limit, you would need to have a lot of faith in the bank.
I have a lot of confidence in Vanguard's and Fidelity's money market operations. They are massive, have low costs, and don't take bad risks to boost yield. Vanguard and Fidelity have closed their government money market funds in order to keep new investors from driving down yields even further. Vanguard's prime money market fund is yielding 0.04%, while its tax-exempt money market fund is yielding 0.08%.
At Fidelity, a $25,000 investment gets you into Fidelity Money Market Fund