As my name might indicate, I live down here in Kochi. If you want events to aim at, there are a few in Shikoku. The best place to check is Sports Entry, the Takamatsu/Tokushima Cycling Federation and your local bike shops, assuming cycling events are what you want to do, though of course Sports Entry covers every type of sports event. I know of a few in Takamatsu, but with the travel time from here, it becomes nearly a whole day - hard to justify with a little kid - and I always think the driving time coud be spent cycling instead. There aren't a lot of actual races, but there are an increasing number of 'sportive' style things. The Tour De Nishiawa is probably the best one around on that basis, but the event sells out in, literally, minutes. Also, there is one around Awajishima that might appeal, but when you can do it for free, the 10,000 fee seems a bit excessive. Certainly having a goal adds focus; persuading myself to go to the pool 2 or 3 times a week is much easier with the aim of a triathlon and a knowledge that my freestyle sucks badly, and that if I can sort it out, I can be competitive age-group wise.
Is there any reason why you just ride in the gym? Here, the roads are generally all in a high condition, and once you get out of the city, traffic is minimal. Lovely conditions to ride. I don't worry for my safety (that feeling of vulnerability) like I do in the UK. If you want someone to ride with, then your local bike shops should organise weekly rides which are usually open for anyone to join. The local ones here accomodate beginners, and people of all ages, so if you are worried about being left behind, don't.
Based on more information, if the goal is health, then the most common things to watch as you age are loss of muscle - your weights is fine for this, though like the other comments, I would question the need for 3 times a week; reduction in aerobic capacity (specifically maximal aerobic capacity. I was reading something recently that proposed including VO2 max tests in health check-ups) - intervals aiming for the 0-3 syllable range is best for this; and preserving bone density - I would add in some impact exercise for that, e.g. running, though some people argue it is not necessary.
Like the comments on slowtwitch, real overtraining is very hard to achieve; overreaching is perfectly possible, but having one bad session could be due to so many different factors, that it doesn't necessarily indicate anything.
Being a vegan shouldn't cause a problem, as there are (I think) pro-triathletes who are vegans. Just make sure your iron levels are sufficient, which is where meat helps, and milk is very good as a recovery drink. Don't worry about sports supplements, they are completely unnecessary.