While I don't doubt that the gym can offer things thta other approaches can't, I think the you pay a lot for this and really have to be disciplined, have reached the limits of what you can do otherwise and know what you want from attending for this to work.
Personally I'm in a similar situation. Legs get a lot of use on the bike (albeit typically low-load, high-cadence so more endurance-focussed than strength) but my upper body has always been weak and aesthetically unappealing.
Being tight, undisciplined and disliking of gyms I like body weight stuff / calasthenics and it seems this can take you very far if you stick to it, although can sometimes be difficult to get into due to the lesser control over the weight on offer.
It seems that all the old-school approaches still hold water - aim to push and pull in all directions with the core exercises being press-ups, dips, chin-ups, pull-ups and sit-ups or hanging knee-raises. Some of these are harder than others and there are some intermediate steps to work up to them - using resistance bands for assistance, altering the angle of attack (such as inclined press-ups with the upper body raised to reduce load on the arms), or shorteing lever arms (press-ups on knees).
Some of the gaps left by typical body weight exercises can be filled with gym rings (such as horizontal pulling actions) and I really love the rings I bought a couple of years ago; which can also assist in transitioning to harder body weight stuff (ring rows are good training for pull-ups if you can't do a full one which was one of my reasons for taking this route), while they offer a lot of instability so are great for also strengthening stabilisting / complimentary muscles that would likely get an easy ride on machines were you're constrained to a single degree of freedom.
Finally dumbells offer a lot of value as they're cheap and versatile; while again also offering a degree of instability you don't get on machines and likely being all the better for promoting real-world, useable strength.
There's a ridiculous amount of really good content on Youtube, and plenty of stuff targeted at people like us rather than meatheads just looking to get ripped at all costs.
Good luck
