We stayed at Blue on White Jan-Mar of 2017 and couldn't have been happier with our choice! The apartment is cozy (it is a studio) but at the same time is well maintained and organized into a very usable space. It is decorated wonderfully and has a very nice kitchen area (although the refrigerator is small). The private courtyard was another plus ... a nice area to sit outside as well as a safe place to store our bikes (or the ones included in the rental).
The location, in our opinion, was great. The neighborhood is vibrant and safe. There are several good restaurants within a couple of blocks, Fausto's (the local grocery) is 1.5 blocks away, the laundromat is 3 houses down, and Higgs beach is a short walk or bike ride away, and downtown (Duval area) is a 10 minute bike ride (we loved riding our bikes to get around Key West!) or a 20 minute walk. Taxi's to and from Duval are reasonable (not so much true the other side of White St which is some sort of dividing line) when and if you need them.
Finally, the owners are fabulous, interesting people! They were readily available to address any of our concerns (of which there were only one or two minor questions). On top of that, they are closely involved with Key West happenings, which in our opinion enhanced our stay by making us feel less like tourists and more like potential residents!
We highly recommend Blu on White and would happily stay there in the future!