Damn, are you me? That's basically exactly me, except I'm usually only 4 days a week. Just do upper body as well...it's weird, I used to do legs as well, but it would take me damn near a week to get over the muscle soreness. Only happens with my legs. Well, maybe a little with my chest, but that's relatively minor, and only for maybe a day. But I could not balance doing legs in the gym, as well as trying to ride. So I gave up, and figured I was getting enough of a leg workout with my riding. The only thing I do now for legs is some work using a plyo box. We built one out of plywood, and just do basic stuff like step ups and jump ups, things like that.

To the OP, if you don't want to pay for or go to a gym, there is a LOT of different workouts you can do at home. Cyclists tend to have underdeveloped upper bodies, and unless you are seriously serious about keeping weight down for racing, it's extremely helpful to balance your riding with some upper body weight training. I do pay for a gym, but I started off years ago by trying to get into bodybuilding (doesn't really work on an ectomorph like me, unless you get into some bad juju!). So, I'm kind of used to going to an actual gym. Lift mostly free weights, dumbbells more specifically, and keeping good form and quality reps, 12-15. Keeps me from getting too "swole", but I don't look like a typical noodle-armed cyclist. You could probably could get away with one of those door jamb pull up bars, some adjustable dumbbells, and some kind of adjustable bench, you'll be able to do a lot of different exercises just with those things.