If your money market funds are short-term savings or an emergency fund, you might consider moving them into an online saving account. You can get interest rates close to 1% (often above 1% in higher-rate climates) and your savings are completely safe and easily accessible. Online banks also frequently offer perks such as direct deposit, linking with your checking account, and discounts on other services you might need occasionally (i.e. money orders or certified checks).
If your money market funds are the lowest-risk part of your diversified long-term portfolio, you should consider how low-risk it needs to be. Money market accounts are now typically FDIC insured (they didn't used to be), but you can get the same security at a higher interest rate with laddered CD's or U.S. savings bonds (if your horizon is compatible). If you want liquidity, or greater return than a CD will give you, then a bond fund or ETF may be the right choice, and it will tend to move counter to your stock investments, balancing your portfolio.
It's true that interest rates will likely rise in the future, which will tend to decrease the value of bond investments. If you buy and hold a single U.S. savings bond, its interest payments and final payoff are set at purchase, so you won't actually lose money, but you might make less than you would if you invested in a higher-rate climate. Another way to deal with this, if you want to add a bond fund to your long-term investment portfolio, is to invest your money slowly over time (dollar-cost averaging) so that you don't pay a high price for a large number of shares that immediately drop in value.