Other than needing a place to live, I've never been much of a real estate guy so I can't claim to know whether buying a rental property would be a good move. In the stock market there is obviously a LOT of short term risk at any given moment, but in the long run you can more or less count on your investment appreciating.
Intuitively I would guess the rental property is also fraught with a different sort of short-term risk for you in that for it to pay off you might need to stay in the area for a while and you don't know for certain that will be the case. If you wind up moving you might need to sell at an inopportune moment.
Were I in your shoes, and I were confident I could keep my expenses down, I would likely keep some cash to cover unexpected emergencies and invest the rest in the stock market. If you kept 15K, you could then buy $100k worth of SPY shares (S&P 500 ETF, i.e. the S&P 500 index). This would result in about $2,000 per year in dividend payments, more or less independently of what the market does, that you could treat as income or treat it as savings and reinvest it in SPY.