The way it looks to me, BW, there are two things a gym provides:
(i) a track for cardio. There isn't a single machine you need, unless you have very special joint issues, that is better than just plain ol' running. But the catch is, ordinary jogging as per the mantra of twenty years ago is by far less efficient than high-intensity, interval-based routines. If you work out a demanding interval routine for yourself, then for most of year you should be able to use streets, parks and so on as your running ground. Conclusion: you don't really need the gym for this.
(ii) weights for resistance training. You cannot get stronger unless you train resistance, and advance your weights upward on a regular basis. I suspect you haven't done serious weight training before, so you're in a good position: a simple, rugged bench and a few pairs of dumbbells will be all you need for a bit (and someone to spot you, preferably). Gyms are great, really essential, if you're already weight-training and reach a level at which you need to use barbells, preferably in a protected environment such a power rack, where you can lift ridiculously heavy weights safely without a spotter because the cross-bars on the rack protect you if the weight falls. But if you haven't reached that point, you can work out productively for at least a year, probably, just using dumbells and a high quality bench that you can keep at home in your basement. Don't know what the going rate is, but they're way, way cheaper than a gym membership, and you don't have to deal with the logistics of packing your stuff and making it out the door—which is, for a lot of people apparently, the hardest part of the deal
TKD, on the other hand, you can't teach yourself. You need the dojang, and your instructor. In short—no comparison. Stick with your TKD program and work the gym program into your home schedule as much as you can.
