I wouldn't worry about wearing the same gear to the gym all the time - (as long as it is clean LOL), a lot of people have a gym outfit.......
I don't know where you live, but if you are somewhere in the country where you can ride a bicycle around country lanes or whatever then buying a bike is a good way to get the cardio fitness going.......... but it isn't much fun riding on the main roads so it really depends where you live.
Also you can buy some dumbells and just do some weights in your bedroom....... I mean you hardly need any space at all to store a couple of weights. You could do squats, pushups, situps, bicep curls, shoulder shrugs, calf raises, Lateral Raises, shoulder press, Front Raises..... etc etc etc, and you don't even need a bench for most exercises, just the dumbbells a private space and possibly chair.