Hey Ely, been spending most of my time in Steamboat for the past 7 years, and is where I first started climbing. Amazing little mountain town with the usual housing shortage. But it is in a great spot with decent climbing, skiing, kayaking, biking, and hiking all close by. The only thing is that none of it is really spectacular, except for maybe the snow, but even then the skiing does not get very steep so after 700+ days I'm kinda over it.
But none of it is bad! Climbing is never crowded, even on weekends, with plenty of options within an hour. New trad leader myself but i travel all summer now so I haven't done any trad lines but I know of a good bit of climbs.
Literally right in town there is a few fun but short top rope climbs along butcherknife (also name of great brewery in town) creek. Blob rock near fish creek falls is about 20 minutes to get to, has some sport lines on it.
North of town seedhouse road has a lot of climbing, about an hour at the longest to get anywhere out that way, good mix of sport and trad I believe.
South up rabbit ears there are a lot of areas as well, quite a few domes and some fun climbing along muddy creek as well. Another good dome towards sarvis creek as well.
Climbing gym just opened about a week ago, so stoked to have that for the winter. I think it was about 60 a month or so.
While access is good, and there is enough to keep you climbing, like I said not much of it is really outstanding. But I really do love the town. And then if you're willing to travel a little: about 2 hours to the poudre, 2 hours to 10 mile west of Silverthorne, a little more to Glenwood canyon, probably 2.5 to rifle, 3 to vedauwoo, and 3 hours to the front range.
I hope that's helpful, I'd be happy to answer any more questions or try and find you some climbing partners