Mountain Biking in the spring/summer/autumn...
Buying used on Mercari or Yahoo auction helps to make the hobby very affordable. If you buy an 'enduro' style bike, you'll be just as happy cruising the streets/roads, exploring mountain trails or hitting the downhill parks like Fujimi or Iwatake... They're like the jack-of-all-trades for bikes.
Take care of your bike and that one-time fee will pay off in the long run...
Late spring/summer/early autumn is perfect for stand-up-paddle boarding... Again, Mercari and Yahoo auction have bargains on inflatable SUPs, but I ended up buying new from Amazon US and even including shipping, the price was ~$400 less than the same model board here in JP...
Once you have a board, rivers, lakes, and the sea are all fair game for adventures or lazy days in the sun... Plus, it's easy to take the kids out on them too...
I live out in Nagano so I guess hiking is up there as one of the best affordable hobbies... Sure it's ideal to have some nice shoes/boots but it's not a requirement... If it hasn't been raining in the days prior to a hike, you could easily get away with trainers/sneakers.
I take my ENO hammock and see if I can find the coolest spots to take breaks and take in the views...
10years ago I bought a 'pull up dip station' from Rakuten for maybe ¥15,000 and the thing is awesome for doing a little calisthenics workout...
Pull-ups, chin-ups, dips, leg-raises, pushups, and you can make little variations to those exercises -hand spacing, isometric holds etc.
I keep mine outside on the patio -I had to replace the cheap padding due to the affects of the weather, but 2 pieces of wood, some thick/firm foam and some decent all weather glue from the local Home Depo store (which must've cost me less than ¥1000), and it has been absolutely fine!
Or, pick up a set of olympic rings with straps and now any tree, playground, gazebo/shelter is your gym! Working out with rings is awesome -highly recommend!
Lastly, make a friend with someone that lives just down the road who built their own indoor climbing gym and go there for free
Yeah, I lucked out on that one...