REIT arguments are usually pro-diversification, but you don't need to diversify farther than index funds.
I should mention that the last stock pick I have in my not-play-money portfolio is O Realty, generally considered blue-chip and nowhere near its silly high, and still expensive and with a miserable performance the last two years. It's in a Roth, which I keep as a counterweight to a down payment I also have saved in stocks (I don't know when I'm going to use it yet). In general, though, I don't really recommend REITs as necessary. I liked the idea a long time back of having something in real estate without being a landlord... looked at Iron Mountain, Apple Hopsitality, STAG... and over time I realized I was just paying extra commissions to play a game I shouldn't bother playing.
I can say, however, you definitely do NOT want to do it outside of a Roth, if that and taxable are your only options. Dividends from REITs are regular income, taxed at your regular tax bracket, not qualified dividends. Unless it's a Roth, where none of your gains get taxed.