Like hypergolic said - Firehouse is overrated. Their food is ok, but their beer has been subpar lately. Independent Ale House is a must if you like craft beer. Crow Peak Brewery in Spearfish is South Dakota's only real brewery.. they can and distribute throughout the area. Downtown Rapid City has really been revitalized - lots of shops and bars to visit.
A really nice hike is the Spring Creek Trailhead of the Centennial trail. It's right before Sheridan Lake Road meets Highway 375 (Google Maps). Best way to take it is start at the trailhead and head towards Sheridan Lake, once you get to the spillway, head south over the dry/overflow area and pick up the Flume Trail - follow that through a tunnel then take the next left fork to head back to the parking area. Really wonderful loop that takes a few hours, crosses a couple streams, walk along the cliffside, and the tunnel! One of my favorite trails in the hills. I made a rough estimate of the path in google mapmaker (Google Mapmaker) not sure if it'll be updated by now or not.
Mount Rushmore is worth going to if you haven't ever been - it's only 15 miles outside of Rapid City. Cost to park is something like $8 if I recall.
Enjoy your few days here!
Edit: Forgot about Spearfish Canyon / Roughlock Falls -- should be beautiful this time of year with the fall colors!
Hike it from the north, at Palmer Gulch, across from the KOA, along 244 just west of Mt Rushmore. It's longer and much more challenging.
There are several hiking apps, like All trails with it's web page.
Hey man, I'm a decade older than you and I've done similar things although the person moved with me. I found people just by getting involved in places similar to the Y and using the website meetup.com. I'm looking to move to Rapid City and if I remember from checking meetup.com over the summer there are a few hiking and other hobby groups there. What people do in the winter is beyond me though.
Although I did see an indoor climbing range which seemed cool. This of course costs money so it all depends on you budget. Just go for whatever free trials you can and make the most of chatting to people while you're there.
Hope is not lost!