Basalt is not a bad location. I stayed in Basalt both times I went to Aspen. Personally, I prefer Basalt over Aspen town or Snowmass village. It is a nice quaint small town outside of Aspen. I like it alot and would stay there again if visiting Aspen.
From Basalt or Carbondale to Aspen 4 if driving:
1) Park at Brush Creek Park and Ride Intercept Lot (as Tony said above). Catch free bus to up valley - Snowmass, Aspen.
2) To Buttermilk - parking is free. lot may be full if there is an event going on e.g. the x-game. In that case, park at Brush Creek Intercept lot and take bus to Buttermilk.
3) To Highland - Can park at Buttermilk parking lot and take free shuttle to Highland, only ~10 min. shuttle ride, it is practically "next door". Shuttle runs every 30 mins. Past year I visited Highland, parking was free if more than "x" # of people per car. Worth a call to Highland to check.
From Basalt to Aspen 4 if taking bus:
1) To find lodging, use Aspenalt Lodge address as your reference, since it is very close to the bus stop. It is an "older" hotel.
2) Basalt Mountain Inn is further in Basalt town, longer walk to and from bus stop, but I think it's still manageable. Newer compares to Aspenalt.
3) The Element Hotel in Basalt. Even though it advertises location in Basalt, it is actually in El Jebel, one bus stop further from Basalt town. Location is very good since there is a bus stop in front of the hotel, worth considering. Room has kitchenette, Whole Food supermarket and restaurants within walking distance of the hotel.
4) If using Airbnb / VRBO, I'd ask how close it is to bus stop (or use Aspenalt hotel as reference point). Some places are too far to walk to bus stop.
Lodging options in Basalt is more affordable.
5) Need to pay bus fare if get on bus in Basalt / Carbondale (it is only free from Brush Creek intercept lot onward). You can buy "Stored Value Card" to pre load, it can be purchased at most bus stops (e.g. Brush Creek Intercept Lot, Basalt town stop).
I found the Aspen bus system very good. It runs frequently and most bus stops have digital screen displaying next bus arrival time. I know approx wait time without downloading the App.
For comparison, in my opinion, Aspen bus system is far better & superior than bus system in Park City.
I don't know about Carbondale since I never stayed there.
Snowmass has first track at 8 am. You need to reserve since it has capacity cap, you can only sign up a wk in advance. Snowmass will call you to confirm reservation the afternoon before. 1st track meets at Elk Camp gondola 8 am, then to Alpine Springs chair. One can get 3 runs in before 9 am regular chair starts.
For MCP passholders, if you want to do first track, make sure you set up lift ticket the day prior. Ticket window opens 8:15 am, 1st track meets at 8 am.