Just want to respond here one more time, because I'm a Virginian through-and-through and I don't often get to talk about why I love places. Big fan of NC too; half of my family is from eastern NC and I personally really like visiting OBX, Raleigh, Charlotte, Asheville, and Winston-Salem.My wife and I have very different interests. My main hobbies are poker, some outdoor stuff like hiking and casual sports, and watching sports. She loves to travel, visit museums, and the arts. We don’t want to live in a big city, but want easy access to a city.
Live in Richmond, VA now and other than poker it fits your description big-time. There may be a poker scene (@Lil Tuna and @grebe) but haven't dedicated a lot of time to finding it. I grew up in Virginia Beach and Richmond is a way cooler city (only thing I miss a ton is the beach). Spent most of my time in undergrad around Charlottesville which is beautiful but the areas don't have nearly as much activity.
In terms of outdoor stuff, the main draw is the James River. I think Richmond is the only "major" city with class 4 rapids running through it. Lots of activities surrounding the river just next to the city. I feel like almost everyone that lives here is into outdoor activities. Not sure what casual sports means, but unfortunately (for me) Richmond probably isn't the biggest sports town. VCU and UR are the local colleges and there just aren't many professional teams around except the ones in DC (although that is only 2 hours to the north). UVA is an hour west. 1-2 hours away to the west you have great/easy hiking in the Blue Ridge Mountains and 2 hours to the east you have the ocean. Can't say much about bourbon, but there are over 30 craft breweries in Richmond - it's incredible in if you are a beer guy.
In terms of visiting museum and the arts, there are a few surprisingly good museums locally. The best one is the Virginia Museum of Fine Arts. In the past few years since I have lived here I have had the opportunity to see exhibits of Edward Hopper, the terracotta army, and sunken treasures of Ancient Egypt (to name a few). Probably the bigger draw from a museum standpoint is the face that DC is just an hour north with all of its museums. Will also add that Williamsburg in an hour east - colonial Jamestown is a pretty neat trip.
I really think that Richmond is a gem that used to be hidden and now is starting to be discovered. It used to be run-over by crime 20-30 years ago (murder capital of US in 1997) but that aspect has significantly improved. Don't get me wrong there is still crime like any city, but nothing like there was. Anyway, I'm obviously biased because I live here, but I think it's a great city - not often that I get to discuss it!
In terms of Virginia weather - it can be great if you like seasons. I haven't been to Ohio, but VA summers are like walking through water most days due to the humidity. For people from here, it's no big deal cuz you get used to it. Most of my friends from the west coast absolutely hate the humidity. Winters get the occasional snow which sucks to me, but some seem to like it. Spring and Fall are really the highlights from a weather perspective. I feel that VA and NC are pretty similar in this regard. I think I'd like the climate of somewhere like Charleston, SC better from a year-round perspective.