An answer is highly dependent on your risk tolerance of course, but have you considered opening a brokerage account at Schwab or Vanguard? Every month, I take any excess cash over my "emergency fund" level and throw it into a dividend aristocrat ETF. You could always automate something like this through your work's direct deposit system too.
EDIT: You could also open a Roth IRA. The limit is only $5,500, and you don't get an up-front tax benefit, but you can always take out the original amount for a house later on if you really need to.