I find it hard to believe that there isn't always some corner where a Strida could stand up against. Even if you don't ask staff to look out for it, gyms aren't generally crawling with bike thieves. If it bothers you enough, lock it with a lightish cable lock in the folded position so it can't be unfolded, such as through both wheels, and just lean it.
Having read through the replies thus far recieved (and I appreciate every one of them) I do have to once again point out that the focus of this thread is simply to determine a good way of locking the Strida outside (and by good, I mean as good as a regular bike, be that as insecure as it may be). While I realize this is a folding bike forum, and folding bikes, by their very nature, encourage a sort of do-anything, go anywhere resourceful attitude in terms of omnipresent transport convenience, I never intended this thread to discuss the merits/disadvantages of leaving the bike vs. taking it with you.
As a concession to those that DO want to question my facility for infiltrating situations I have posed as problems with the bike in tow, I have found that around 85% of the time, taking the bike along poses virtually no difficulty, with a speculated far lesser risk of theft than street locking, especially at night;
That said, the problem lies not so much in terms of real-world inconvenience or lack of space (in theory, keeping the Strida out of the way but in sight at the gym would be a very simple task), but more in the sadly commonplace bureaucratic mentalities of minor level "maintainance" employees. Much like the "following orders" creedo of many a hierarchy, rules must be obeyed lest a higher-up cause problems. That means, "bikes," which in this case are smaller than the massive wheeled duffel someone else brought on, are not allowed on the bus according to "the rules." That means I'm not allowed in the gym with it (which, if I'm not mistaken, is supposed to promote an active lifestyle), just because it has petals and a seat, and maybe, because folded, it confuses the simple mind telling me "no." I could get into all of the historical and political parallels regarding this type of knee-jerk response I've sadly come to expect, despite my attempt at nonchalance (or the force), but I think you get my point, rant over, and sorry for so many "quotation marks."
So, sounds like the wheels, with a ulock, win so far. Anyone try the cufflock idea? Thanks again for past and future responses.