June 1st is “off-cycle” so there will be limited choices, but I think since you’re looking at newer buildings you may have more luck. There are a lot near alewife (on the red line) that are being built so those may be a good option, and less expensive since a little outside the city. Kendall sq is another location on the red line where I’ve seen newer buildings, but haven’t seen many in harvard or central sq. Some of these buildings may also be able to send you virtual video tours.