I'll honestly try to answer this without ranting.
FWIW I'm currently in Abilene after spending ~5.69 years at Ellsworth (and ~1 year before that at Dyess).
Personally, I vote for Rapid City all the way and twice on Sunday. The city is vibrant for a small town and is in the middle of a great little growth spurt. Although it's population is ~75000 (not counting the Lead/Deadwood/Sturgis peeps), which is smaller than Abilene, since it's the only "big" city for about 350 miles in any direction, it's got a lot going for it. There are about twice as many places to eat with a much better variety than in Abilene. It's got a good small local arts scene, all the shopping you need, and is in the middle of a downtown renovation project that's bringing some awesome small business growth (both shops and restaurants/bars). There is a semi-pro hockey team and the games are a blast.
In South Dakota, you can shoot in just about any state park, and CCWs are $10 with a mil ID (reciprocity in something like 17 states). The folks are mostly conservative but with a libertarian streak, so state government stays out of your business for the most part. Schools are about average. I don't have kids but my friends who do usually don't complain much.
Winters are harsh, although the last few have been fairly light. Expect a good solid 2 week period in late January or February where temps don't get above 10 degrees. It's not unbearable and you don't need anything crazy like engine block heaters. You will get sick of the wind and learn the true meaning of wind chill.
You mentioned the outdoors activities so I won't harp on that. Tons to do outside. Lots of tourist spots to hit up - Rushmore, Crazy Horse, the Bandlands, and Sturgis to name a few. Deadwood is a blast. There is skiing available at Terry Peak about an hour or so west of town.
The local airport has ~5 different carriers. You will still pay regional airline prices, but you have decent options for flights.
Since the only two B-1 squadrons are ops squadrons, the base seems to be more focused than Dyess. For the last 6+ years, Ellsworth has had a squadron deployed for 12 out of every 18 months. MX rates are generally better than Dyess. There is currently a big airspace initiative that would give Ellsworth the biggest training airspace in the CONUS (about 2x bigger than UTTR/NTTR). If that goes through, flying will get even better. The backyard MOA (Powder River) is better than at Dyess (Lancer), and allows for low level training.
In short, I had a blast at Ellsworth and would go back in a heartbeat.
As for Dyess, I'll just tell you the reasons why I don't like it and you can decide if they apply to you or not.
Abilene is so anti-progress it boggles my mind. The city council actively works to prevent new businesses, especially restaurants and bars, in some misguided attempt to prevent the city from becoming like "the metroplex" (which is an insane notion). The downtown, and I use that term loosely, is usually a ghost town after business hours. There are two decent restaurants downtown, but you'll spend ~25 minutes driving there from the good areas of town where everyone lives.
Bars must close by midnight on weekdays and 1AM on weekends. I realize this isn't a huge concern for a lot of dudes but it says something about the local population and their values.
You can't swing a dead cat without hitting a church - some VERY conservative. Again, might not be a negative for some.
It's Texas - west Texas at that, and you can't easily escape it. American Airlines is the ONLY carrier at the local airport and routinely cancels flights for weather or lack of aircraft availability.
The flying at Dyess is sporadic and frustrating. MX rates are consistently low. The scattered nature of the units on base (schoolhouse, weapons school, test, and one ops squadron) seem to prevent the wing from having a real focus. The local airspace sucks - to get good training accomplished requires scheduling at least two or three different ranges.
On the plus side, there is a zoo. You are also 2.5 hours from Ft Worth, 3 hours from Dallas, and 3.5-4 from San Antonio and Austin.
I should state for the record that I hate the state of Texas with the burning passion of a million suns. Hope this helps.