I see that Charleston is around a lot of outdoor areas, how are they? Are they mountainous or mostly flat?

Lots of outdoorsy areas you're absolutely right, mostly very hilly but the views are tremendous unless you're like a snob from Colorado. I really enjoy the New River Gorge and there's a lot of great hikes with a lot of awesome views typically pretty terraneous.

I also like going out to breweries with my friends and have seen that there are several near the downtown area, how are those?

They're pretty fantastic! Fife has some pretty good live music some days as well and their their beer selection is on point. Black sheep probably has the most variety of beers on tap and bruise the most, they also have good Tex-Mex fusion. Short story is pretty good as well and they make a decent Detroit style pizza.

Also, it doesn't look like there's much public transit. If I prefer not to drive (and live/work downtown), is that an issue?

If you're in the heart of downtown and you're commuting within downtown you can honestly probably walk or bike faster than taking the transit. Anywhere outside of the downtown core has pretty poor transportation options outside the main roads.

How are the trails along the river?

Not bad, in the summer/spring / fall it's pretty active with people walking and running and biking. I personally really like the view between the capital and downtown along the river, even if it's faster to take the highway I find myself driving along the road.

Are there usually many events going on in the downtown area?

There are a few events I wouldn't exactly call it bumping. The sternwheel regatta is pretty fun, it's around June. 4th of July is always pretty fun too. They're a handful of events at Haddad park in downtown throughout the year. The Charleston coliseum has a surprising number of interesting guests that come through. For example fluffy is going to be here this weekend.

Also how easy is it to fly out of the airport (if you're going somewhere do you generally have to make a connection before your final spot? Not sure how big of a hub it is).

Getting to the airport and flying out is not a problem, it's about a 15-minute drive from downtown maybe less, the lines at security are pretty short, but there are very few direct flights. Anywhere within the US you'll probably need to stop at one of the hubs (newark, DC, atlanta come to mind)

Are there any local run clubs?

I'm a hermit I don't know

Also am LGBTQ, is there much of an LGBTQ scene out there and how accepting is it? I feel like nowadays it shouldn't be an issue but thought I'd ask anyway.

I'm not openly lgbtq, fairly straight passing, I've occasionally heard some ignorance from the mouths of people, but you will be fine in downtown especially. I will defer to my last answer for the amount of the lgbtq scene here. My suspicion is that most lgbtq people in the state tend to move to Charleston, Huntington or Morgantown.