The beginner's area is known as "Union Creek". The closest accomodations to it would probably be The Lodge, but even that's a stretch. There's a small service road you can use to access Union Creek that's on the mountain side of the building. I ski the road, but you might find that difficult. It's about 300 -400 hundred yards to Union Creek. The lifts in the beginner area are High Point and Kokomo.
The American Flyer lift also services a lot of green terrain and it's much more accessible from lodging. I'll list the accomdations from closest to farthest and rate them for you. The rating are relative to each other and even the worst rooms are probably better than your typical Marriott; rating range from 1-star to 4-stars (****). All of these buildings have hottubs, workout rooms, and underground parking. I've been in all the units in all these buildings:
The Lodge (**) - one of the few true ski-in/ski-out buildings at Copper. It sits right next to the American Flyer lift. Many units have been remodeled in the past decade or so, it's completely possible you'll end up with a very nice room there.
Copper 1 Lodge ( *** ) - right in the heart of things. It was completed in 2001 and all of the rooms are very nice. While I think the rooms are a tad nicer than the next choice, I might shy away from it because half of the rooms overlook Burning Stones Plaza and there's a chance you'll get woken up at 11pm by a snowcat or 7am by music from below. Even though it looks closer on the map than the next choice, I think the short walk is harder.
Tucker Mtn Lodge ( *** ) - a newer building completed in 2000. The rooms are fairly nice and it has a nice location. Walk out the front door, across a very small plaza, ride an escalator and you're on the snow. If you can get a good room here for a good price I'd recommend it. I like how it's situated in the village.
The Cirque ( **** ) - not too far from American Flyer, perhaps 300 yards? Very nice building completed in 2004. It features 2 outside swimming pools. The rooms get nicer the higher you go up.
Taylor's Crossing / Mill Club / Passage Pt ( *** ) - all of the units are roughly the same distance. Mill Club has some wonderful units in it and it's where I like to stay.
There's no free parking at the base of any lifts. If you're a pass holder, or you purchase your tickets in advance, you can drive to the base of the Alpine lift. However, that lift only services blue/black terrain. You can park in the Beeler lot near American Flyer for about $10. It's pretty easy to arrange ski pickup/dropoff from there. There's also a free shuttle that runs from the free Alpine parking lot.