So this is kind of like... a mix of free-ish cardio/strength, so. YMMV, and all that.
Stairs: I'm a big fan of stairs - walking, running, sprinting, prancing, whatever, so long as you get from point A to point B. If you're lucky to have a bunch of stairs near you, in a park or in a stadium, or even in your very tall apartment building - walking down/running up the whole stretch four or five times is an excellent workout (plus, in case of fire, you'll be the first one out the door). If you feel like you really need your butt kicked that day, you can fill a running/cycling backpack with bottles filled with water, sand, or wet sand (note here that metal weights will drag significantly on your shoulders, while you can pack/strap down bottles so the weight is more distributed on your back) and run sprints/walk up a stretch of stairs. It's much more leg-muscle involved than you'd think, and if you focus on flexing the calves when you go up (using the front of your feet on the step, slow and controlled, instead of the whole foot), your calves get one heck of a beating (a good beating!).
Playgrounds - you just have to go when there's no little kids around so you don't look crazy. The monkey bars are pretty awesome for pull-ups. If you're not up to full flat-out pull-ups, most monkey bars tend to be pretty low to the ground, so jumping pull-ups would be a good start (feet on the ground, hands on the bar, jump up and pull). If there's a wooden bench around, you can do box jumps - jump up/down, and if you want you can do it for time. This one I've never tried in a swing, but I've done the movement on the ground. Sit in a swing, grab the chains at chest height. Lean backwards while extending your legs so you're parallel to the ground. Pull legs and chest in so knees and chest meet - like a crunch, only you'll be wobbly and swinging, so it'll make it harder.
Burpees! I hate these and actually gave up on the 100 Burpee Challenge, but these are awesome at working your upper body, lower body, and endurance in general, moreso if you do it for time. Essentially squat + pushup + explosive bounce into standing position.
Band squat: If you have a resistance band, you can tie it around something sturdy at chest height, grab it in one hand and drive it violently down behind you while squatting, like pulling the starter cord on a lawnmower, only... squatting, and down.
Tabata squats. Twenty seconds of squats as fast as you can, ten seconds of rest. Repeat eight times for total of four minutes. You will hurt. (For that matter, Tabata anythings. But Tabata squats... oy.) If you really want to die: do these wearing a backpack with weights.
tl;dr squats, squats, squatty lower body squat squat squat.
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Stairs: I'm a big fan of stairs - walking, running, sprinting, prancing, whatever, so long as you get from point A to point B. If you're lucky to have a bunch of stairs near you, in a park or in a stadium, or even in your very tall apartment building - walking down/running up the whole stretch four or five times is an excellent workout (plus, in case of fire, you'll be the first one out the door). If you feel like you really need your butt kicked that day, you can fill a running/cycling backpack with bottles filled with water, sand, or wet sand (note here that metal weights will drag significantly on your shoulders, while you can pack/strap down bottles so the weight is more distributed on your back) and run sprints/walk up a stretch of stairs. It's much more leg-muscle involved than you'd think, and if you focus on flexing the calves when you go up (using the front of your feet on the step, slow and controlled, instead of the whole foot), your calves get one heck of a beating (a good beating!).
Playgrounds - you just have to go when there's no little kids around so you don't look crazy. The monkey bars are pretty awesome for pull-ups. If you're not up to full flat-out pull-ups, most monkey bars tend to be pretty low to the ground, so jumping pull-ups would be a good start (feet on the ground, hands on the bar, jump up and pull). If there's a wooden bench around, you can do box jumps - jump up/down, and if you want you can do it for time. This one I've never tried in a swing, but I've done the movement on the ground. Sit in a swing, grab the chains at chest height. Lean backwards while extending your legs so you're parallel to the ground. Pull legs and chest in so knees and chest meet - like a crunch, only you'll be wobbly and swinging, so it'll make it harder.
Burpees! I hate these and actually gave up on the 100 Burpee Challenge, but these are awesome at working your upper body, lower body, and endurance in general, moreso if you do it for time. Essentially squat + pushup + explosive bounce into standing position.
Band squat: If you have a resistance band, you can tie it around something sturdy at chest height, grab it in one hand and drive it violently down behind you while squatting, like pulling the starter cord on a lawnmower, only... squatting, and down.
Tabata squats. Twenty seconds of squats as fast as you can, ten seconds of rest. Repeat eight times for total of four minutes. You will hurt. (For that matter, Tabata anythings. But Tabata squats... oy.) If you really want to die: do these wearing a backpack with weights.
tl;dr squats, squats, squatty lower body squat squat squat.