No gyms, how about MMA gyms or kick boxing, they will teach you the basics.
I would avoid Karate gyms.

Lots of places offer boxer-cise classes which is boxing training in a circuit.
You do one of those classes I am sure the instructor will help you with regards to punching and getting started.

Skipping and running needs no equipment.
Same with shadow boxing.
Google body-weight exercises to find information on getting strong.
Doing army style training will get you in shape, sit-ups, running and press-ups.
You can get army fitness training schedules direct from their websites.

But it is best to get some 1-on-1 tuition, so you know if you are throwing the punches correctly.