I have looked at a few, the fees and the opaque structure scared me away. I would like the control, of being able to sell my share on the open market at any point (at close to face value, obviously) and being able to benefit from a proportion of rental income where ROI < 20 years.
Avoid the private REITs and buy one that's publicly traded. Also avoid mortgage REITs, those lend money (vs owning buildings).
Here's a simple screen for office REITs with a market cap over $300m on the NYSE (note that there are other types residential/retail/medical/etc under the "industry" filter):
How are REITs opaque? You can find out exactly what they own and there is no easier way to get get in and out of a property investment than through a REIT, especially larger ones.