1. THERE IS NO PARKING AT AJAX, and you will be ticketed for parking on the Aspen streets. I don't think there is parking at Highlands either. Park at Buttermilk each day and take the shuttle to where you want to go. You may want to drive and park at Snowmass, as that is the only mountain that is any real amount of distance away from the Buttermilk parking lots.
2. Its pretty hard to give you advice with just "like skiing blacks" to go off of. What is your home mountain? What type of runs do you enjoy skiing? Bowls? Moguls? Powder? The three major Aspen mountains are at the top end of challenge for major resorts. A "Black" run can mean completely different things depending on the ski area rating it, so without knowing where you are skiing, we can't really give you any idea of where to guide you. In addition, the Aspen mountains have a LOT of vertical, so there is a good chance you will be skiing runs that are a lot longer than you are used to. There are plenty of advanced and expert runs at Aspen that drop for 2000+ vertical feet before you get a chance to bail out to an easier run.
Elevation is also a consideration. The recommendation is to spend a day acclimating at altitude before you go and exert yourself, or some people in your party can have a bad time. Its not feasible for a lot of people to do this, so if you can't I would start out at Buttermilk to get a feel for what you are skiing. Nothing keeps you from taking ten minutes to jump the shuttle someplace else if you want more challenge that first day.
If not Buttermilk, I would start at Snowmass. There is a lot of terrain there, and Snowmass has a ton of good intermediate terrain, as well as a lot of really advanced stuff up top. Basically, Snowmass can be as wild or as tame as you are comfortable with, and it will help give you a feel for how they rate trails.
Ajax and Highlands have basically no true beginner terrain, and both mountains have a lot of vert and a lot of pitch. Ajax has more of a european feel, especially if it hasn't snowed- lots of moguls and stuff that appeals to hard-snow guys. Highlands has steeps, with a lot of very steep gladed runs, as well as obviously, Highland's bowl.
If you can hack it, hiking Highlands is an experience, but you really want to make sure you are physically capable of hiking 1,000 vertical feet on a knife ridge in ski boots, let alone capable of skiing 50*+ pitches for 1800 vertical feet down. If it has snow, it is epic. When skiing the bowl, stay off of the Y-zones unless you catch a day with 9+ inches that morning- it is south facing and gets pretty hard quickly. If there has been snow in the days before your trip, the rest of the bowl is usually good- they stagger out opening the bowl after storms to make sure the whole bowl gets uniformly ski packed for avalanche control, which means after a large storm, you can still get fresh tracks for days after as the ski patrol does staggered openings.
Highlands has a snow cat that they use to transport ski patrol out to Highlands bowl, and you can ride the cat out to the beginning of the knife ridge, which saves you about 1/3 of a mile on the hike. However, this only covers the flat part of the hike, and on busy days, it can be faster to walk it rather than wait in line for the cat.