I love my city but there are some steep hills - because of my weight and my lung capacity, I'm reluctant to spend much time climbing them (but I also love doing it!). How can I build lung capacity and leg endurance in the gym?
Arguably, the best way to build up work capacity for walking / running the hills in your city, is to go out and either walk or run the hills. The very act of doing the activity itself will, over time, condition you to it.
If you want gym specific exercises to help, then you should be looking primarily at things like squats (both weighted and body weight), split squats / lunges and step up variations to strengthen your legs (doing these with effort will also help with lung capacity), and pretty much any form of cardio to build lung capacity (walking on an incline treadmill, exercise bike, stepper, even something like rowing will help).
That's a pretty generic answer as you haven't provided that much information, so I don't know your familiarity with the exercises, level of fitness, etc.
If you want more specific, then when you get into the gym, do a decent warm up, including mobility exercises for the general hip area, including the hamstrings, then move onto some strength work.
I would say do Bulgarian split squats in alternating sets with step ups; the idea being that both should roughly mimic the action of walking up hill but with differing levels of specificity, then follow that up with several sets of sled push / pulls if you have access to a sled (unfortunately, not many gyms do), and finish off with something like some low effort incline treadmill walking, or lower effort exercise bike work, just to get the blood flowing around the legs.
Do that a few times a week, after the first few times, you'll probably find you get some pretty bad DOMS, if so, still head into the gym, but just do some warm up exercises followed by lighter treadmill or exercise bike work, again, to get the blood flowing.
Honestly though, if you really want to walk the hills where you live, head out and do it. Nothing can compare to getting out in the fresh air and being active (obviously fresh is relative, depending on where you live ;)
During each marathon training cycle, our running group always incorporates at least one hill workout every other week. (For the Twin Cities Marathon we do one per week). There is no set time to do our hills, instead, we concentrate on good form going up and down the hill. In the beginning, I may run slow and I put all my focus on form. I always try to complete the distance even if I walk a good portion of the hills.
At the end of the cycle, I find that the effort is much easier than it was in the beginning and the hills pay off even on a flat course. (Like Chicago).
I would use my running workouts to gain endurance and gym workouts to gain strength. glutes, hamstring, and quads are good areas to focus on for strength. I have never found that the gym builds any aerobic capacity for hills.
To really build endurance we also mix in an LSD run incorporating hills.
Very workable solution -- Activity specific training.
Your focus should be on increasing intensity, not duration. (the hills will become progressively easier).
- Write down a simple workout plan - something like M W F you'll walk/jog/run up and down your hills.
- Have a plan in mind (a set number of times you're gonna run it - if it's too hard take a break just make sure you finish what you plan).
- Keep it simple. Maybe M and F you run 20 times up and walk 20 times down - Wed do the opposite walk up, run down.