100% fly into Aspen. The next best thing is flying EWR direct to Vail which I've done once and it was pretty convenient. It's about 1hr30m from EGE to Aspen. If you're going to connect somewhere, you might as well fly direct into ASE. DEN is 4.5+ hours away under decent conditions. One Vail pass closure and it'll be a helluva lot longer.
Stay in Aspen if you can. Tons of bars/food options. I love walking around a "real" ski town with my skis over my shoulder. Despite everyone thinking Aspen is all glitz and glamour, it is very authentic. Similar to Telluride and nothing like Vail / Winter Park / etc. As for resorts in Aspen, skip them. They're all $$$. VRBO/AirBnB something. Jay has paid ~$2000 for a week for a 2 bedroom place about a 3 minute drive from the Gondola. If you want a resort, stay in Snowmass, quite a few reasonable slope side options there, but you're more isolated from the fun. Will be more like staying in Teton Village vs Town of Jackson.
My favorite place to grab something quick to eat in Aspen is the "Big Wrap". Cash only. I get the pesto wrapture burrito. I could eat them every day.
As for skiing, I love all 4 resorts for different reasons. For big pow days, Snowmass or Highlands. I'd skip Highlands on a pow day unless it has snowed frequently recently because the south facing stuff (besides "the Bowl") will be firm. Highlands is on a ridge that falls away on both sides. Snowmass has tons of acreage and technically has more vertical footage than JH (4400ft ... the most in the US). The hanging valley wall area and the cirque area will yield pow way longer than any run at JH, granted at lower angles.
If it's a sunny day, I love ripping turns at Ajax (Aspen Mountain) and soaking up the sun hitting some soft bumps, skiing the dumps, crushing turns down the best run of all time, america's downhill, Ruthies Run. Nobody is in a rush and all the slow signs say "relax it's aspen" and you'll see some awesome outfits. If it's been sunny a lot and I've skied Ajax a few days, I'll head over to Buttermilk and rip turns down the Tiehack area with the biggest smile on my face.
I've skied JH 77 times, but I've spent a combined 54 at the Aspen resorts. If I had to pick a place to ski and live for the rest of my life, I'd pick Aspen in a heart beat.